{"id":42,"date":"2021-03-24T18:00:07","date_gmt":"2021-03-24T18:00:07","guid":{"rendered":"https:\/\/stage-wp.10minuteschool.com\/?p=42"},"modified":"2022-03-24T12:25:03","modified_gmt":"2022-03-24T12:25:03","slug":"calculus-in-physics","status":"publish","type":"post","link":"https:\/\/10minuteschool.com\/content\/calculus-in-physics\/","title":{"rendered":"\u09aa\u09a6\u09be\u09b0\u09cd\u09a5\u09ac\u09bf\u099c\u09cd\u099e\u09be\u09a8\u09c7 \u0995\u09cd\u09af\u09be\u09b2\u0995\u09c1\u09b2\u09be\u09b8"},"content":{"rendered":"\r\n

\u09aa\u09a6\u09be\u09b0\u09cd\u09a5\u09ac\u09bf\u099c\u09cd\u099e\u09be\u09a8\u09c7 \u0995\u09cd\u09af\u09be\u09b2\u0995\u09c1\u09b2\u09be\u09b8 (Calculus in Physics)<\/strong><\/h2>\r\n

\u0995\u09cd\u09af\u09be\u09b2\u0995\u09c1\u09b2\u09be\u09b8 \u09b9\u09b2\u09cb \u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09a8\u09c7\u09b0 \u0997\u09be\u09a3\u09bf\u09a4\u09bf\u0995 \u0985\u09a7\u09cd\u09af\u09af\u09bc\u09a8\u0964 \u098f\u09b0 \u09aa\u09c1\u09b7\u09cd\u099f\u09bf \u09aa\u09cd\u09b0\u09a7\u09be\u09a8 \u09b6\u09be\u0996\u09be \u09b0\u09af\u09bc\u09c7\u099b\u09c7 \u09a1\u09bf\u09ab\u09be\u09b0\u09c7\u09a8\u09b8\u09bf\u09af\u09bc\u09be\u09b2 (Differential) \u0995\u09cd\u09af\u09be\u09b2\u0995\u09c1\u09b2\u09be\u09b8 \u0993 \u0987\u09a8\u09cd\u099f\u09bf\u0997\u09cd\u09b0\u09be\u09b2 (Integral) \u0995\u09cd\u09af\u09be\u09b2\u0995\u09c1\u09b2\u09be\u09b8\u0964 \u09ac\u09bf\u099c\u09cd\u099e\u09be\u09a8\u09c0 \u09a8\u09bf\u0989\u099f\u09a8 \u09b8\u09b0\u09cd\u09ac\u09aa\u09cd\u09b0\u09a5\u09ae \u09aa\u09cd\u09b0\u09be\u09a8\u09cd\u09a4\u09bf\u0995 \u09aa\u09a6\u09be\u09b0\u09cd\u09a5\u09ac\u09bf\u099c\u09cd\u099e\u09be\u09a8\u09c7 \u09a1\u09bf\u09ab\u09be\u09b0\u09c7\u09a8\u09b8\u09bf\u09df\u09be\u09b2 \u0995\u09cd\u09af\u09be\u09b2\u0995\u09c1\u09b2\u09be\u09b8 \u09aa\u09cd\u09b0\u09af\u09bc\u09cb\u0997 \u0995\u09b0\u09c7\u09a8\u0964<\/p>\r\n

\u0997\u09c1\u09b0\u09c1\u09a4\u09cd\u09ac\u0983<\/b><\/p>\r\n\r\n\r\n\r\n

\u09aa\u09a6\u09be\u09b0\u09cd\u09a5\u09ac\u09bf\u099c\u09cd\u099e\u09be\u09a8\u09c7 \u0995\u09cd\u09af\u09be\u09b2\u0995\u09c1\u09b2\u09be\u09b8-\u098f\u09b0 \u0985\u09aa\u09b0\u09bf\u09b9\u09be\u09b0\u09cd\u09af \u0997\u09c1\u09b0\u09c1\u09a4\u09cd\u09ac \u09b0\u09af\u09bc\u09c7\u099b\u09c7\u0964 \u0985\u09a8\u09c7\u0995 \u09ac\u09be\u09b8\u09cd\u09a4\u09ac \u09aa\u09cd\u09b0\u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be \u09a1\u09c7\u09b0\u09bf\u09ad\u09c7\u099f\u09bf\u09ad\u09b8 \u09af\u09c1\u0995\u09cd\u09a4 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09ac\u09cd\u09af\u09be\u0996\u09cd\u09af\u09be \u0995\u09b0\u09be \u09b9\u09af\u09bc\u0964 \u09b8\u09c7\u0987 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u0997\u09c1\u09b2\u09cb\u0995\u09c7 \u09ac\u09cd\u09af\u09ac\u0995\u09b2\u09a8\u09c0\u09af\u09bc (\u09a1\u09bf\u09ab\u09be\u09b0\u09c7\u09a8\u09b8\u09bf\u09af\u09bc\u09be\u09b2) \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09ac\u09b2\u09c7\u0964<\/p>\r\n

\u09ac\u09c7\u0997 \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09b8\u09b0\u09a3\u09c7\u09b0 time derivative<\/p>\r\n

\u09a4\u09cd\u09ac\u09b0\u09a3 \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09ac\u09c7\u0997\u09c7\u09b0 time derivative<\/p>\r\n\r\n\r\n\r\n

\u09ac\u09cd\u09af\u09ac\u09b9\u09be\u09b0\u0983<\/strong><\/p>\r\n

\u09ac\u09c7\u0997, \u09a4\u09cd\u09ac\u09b0\u09a3, \u09ac\u0995\u09cd\u09b0\u09b0\u09c7\u0996\u09be\u09b0 \u09a2\u09be\u09b2 \u0987\u09a4\u09cd\u09af\u09be\u09a6\u09bf \u09b9\u09bf\u09b8\u09be\u09ac\u09c7\u09b0 \u099c\u09a8\u09cd\u09af \u09a1\u09bf\u09ab\u09be\u09b0\u09c7\u09a8\u09b6\u09bf\u09af\u09bc\u09be\u09b2 \u0995\u09cd\u09af\u09be\u09b2\u0995\u09c1\u09b2\u09be\u09b8 \u09aa\u09cd\u09b0\u09af\u09bc\u09cb\u0997 \u0995\u09b0\u09be \u09b9\u09af\u09bc\u0964 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09ab\u09b2, \u0986\u09af\u09bc\u09a4\u09a8, \u09ad\u09b0\u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0, \u0995\u09be\u099c \u098f\u09ac\u0982 \u099a\u09be\u09aa \u0987\u09a4\u09cd\u09af\u09be\u09a6\u09bf \u09b9\u09bf\u09b8\u09be\u09ac\u09c7\u09b0 \u099c\u09a8\u09cd\u09af \u0987\u09a8\u09cd\u099f\u09bf\u0997\u09cd\u09b0\u09be\u09b2 \u0995\u09cd\u09af\u09be\u09b2\u0995\u09c1\u09b2\u09be\u09b8 \u09ac\u09cd\u09af\u09ac\u09b9\u09be\u09b0 \u0995\u09b0\u09be \u09b9\u09af\u09bc \u0964<\/p>\r\n

\u0989\u09a6\u09be\u09b9\u09b0\u09a3\u0983<\/b><\/p>\r\n

\u09a6\u09c7\u0993\u09af\u09bc\u09be \u0986\u099b\u09c7, \u098f\u0995\u099f\u09bf \u09b8\u09b0\u09b2\u09b0\u09c7\u0996\u09be\u09b0 \u0989\u09aa\u09b0 \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09a8<\/p>\r\n\\begin{array}{c}\n\\mathrm{x}(\\mathrm{t})=-16 \\mathrm{t}^{2}+16 \\mathrm{t}+32 \\\\\n\\text { \u09a4\u09be\u09b9\u09b2\u09c7 \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09ac\u09c7\u0997 , } \\mathrm{v}=\\frac{\\mathrm{dx}(\\mathrm{t})}{\\mathrm{dt}}=\\mathrm{x}(\\mathrm{t})=-32 \\mathrm{t}+16 \\\\\n\\text { \u098f\u09ac\u0982 \u09a4\u09cd\u09ac\u09b0\u09a3, } \\mathrm{a}=\\frac{\\mathrm{dv}}{\\mathrm{dt}}=\\mathrm{x}(\\mathrm{t})=-32\n\\end{array}<\/span>\r\n

\u09a8\u09bf\u0989\u099f\u09a8\u09c7\u09b0 \u0997\u09a4\u09bf\u09b0 \u09a6\u09cd\u09ac\u09bf\u09a4\u09c0\u09af\u09bc \u09b8\u09c2\u09a4\u09cd\u09b0 \u09b8\u09be\u09a7\u09be\u09b0\u09a3 \u09ac\u09cd\u09af\u09ac\u0995\u09b2\u09a8\u09c0\u09af\u09bc (\u09a1\u09bf\u09ab\u09be\u09b0\u09c7\u09a8\u09b8\u09bf\u09af\u09bc\u09be\u09b2) \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u09c7\u09b0 \u09ae\u09be\u09a7\u09cd\u09af\u09ae\u09c7 \u09a8\u09bf\u09ae\u09cd\u09a8\u09cb\u0995\u09cd\u09a4\u09ad\u09be\u09ac\u09c7 \u09aa\u09cd\u09b0\u0995\u09be\u09b6 \u0995\u09b0\u09be \u09af\u09be\u09af\u09bc\u0964<\/p>\r\n\\mathrm{F}(\\mathrm{t})=\\mathrm{m} \\frac{\\mathrm{d}^{2} \\mathrm{x}}{\\mathrm{dt}^{2}}<\/span>\r\n\r\n\r\n\r\n

\u0987\u09a8\u09cd\u099f\u09bf\u0997\u09cd\u09b0\u09be\u09b2 \u0995\u09cd\u09af\u09be\u09b2\u0995\u09c1\u09b2\u09be\u09b8-\u098f\u09b0 \u09b8\u09be\u09b9\u09be\u09af\u09cd\u09af\u09c7 \u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09c0<\/b> \u09ac\u09b2 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u0995\u09be\u099c \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc\u0983<\/strong><\/p>\r\n\r\n\r\n\r\n

\u09a7\u09b0\u09bf, \u098f\u0995\u099f\u09bf \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u0993\u09aa\u09b0 \u098f\u0995\u099f\u09bf \u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09a8\u09b6\u09c0\u09b2 \u09ac\u09b2 x -\u0985\u0995\u09cd\u09b7 \u09ac\u09b0\u09be\u09ac\u09b0 \u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be\u09b6\u09c0\u09b2\u0964 \u09ac\u09b2\u099f\u09bf\u09b0 \u09ae\u09be\u09a8 \u09ac\u09b8\u09cd\u09a4\u09c1\u099f\u09bf\u09b0 \u0985\u09a4\u09bf\u0995\u09cd\u09b0\u09be\u09a8\u09cd\u09a4 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac \\mathrm{x}<\/span> -\u098f\u09b0 \u0993\u09aa\u09b0 \u09a8\u09bf\u09b0\u09cd\u09ad\u09b0 \u0995\u09b0\u09c7 \u0985\u09b0\u09cd\u09a5\u09be\u09ce \\mathrm{F}<\/span>, \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac \\mathrm{x}<\/span> -\u098f\u09b0 \u098f\u0995\u099f\u09bf \u0986\u09aa\u09c7\u0995\u09cd\u09b7\u09bf\u0995\u0964 \u099a\u09bf\u09a4\u09cd\u09b0\u09c7 \\mathrm{x}<\/span> -\u098f\u09b0 \u09ac\u09bf\u09ad\u09bf\u09a8\u09cd\u09a8 \u09ae\u09be\u09a8\u09c7\u09b0 \u099c\u09a8\u09cd\u09af \\mathrm{F}(\\mathrm{x})<\/span> \u098f\u09b0 \u0986\u09a8\u09c1\u09b7\u0999\u09cd\u0997\u09bf\u0995 \u09ae\u09be\u09a8 \u09a8\u09bf\u09af\u09bc\u09c7 \u09b2\u09c7\u0996 \u09a6\u09c7\u0996\u09be\u09a8\u09cb \u09b9\u09af\u09bc\u09c7\u099b\u09c7\u0964<\/p>\r\n\r\n\r\n\r\n

\r\n
\"\"<\/figure>\r\n<\/div>\r\n\r\n\r\n\r\n

\u09ae\u09cb\u099f \u09b8\u09b0\u09a3 \\Delta x<\/span> \u09aa\u09cd\u09b0\u09b8\u09cd\u09a5\u09c7\u09b0 \u0995\u09cd\u09b7\u09c1\u09a6\u09cd\u09b0 \u0995\u09cd\u09b7\u09c1\u09a6\u09cd\u09b0 \\text {n}<\/span> \u09b8\u0982\u0996\u09cd\u09af\u0995 \u09b8\u09ae\u09be\u09a8 \u0985\u0982\u09b6\u09c7 \u09ac\u09bf\u09ad\u0995\u09cd\u09a4, \u09af\u09c7\u0996\u09be\u09a8\u09c7 x_{i}<\/span>\u00a0 \u09a5\u09c7\u0995\u09c7 x_{i}+\\Delta x<\/span> \u09aa\u09b0\u09cd\u09af\u09a8\u09cd\u09a4 \u0995\u09cd\u09b7\u09c1\u09a6\u09cd\u09b0 \u09b8\u09b0\u09a3 \u09b9\u099a\u09cd\u099b\u09c7 \\Delta x<\/span> \u0964 \u098f\u0987 \u0995\u09cd\u09b7\u09c1\u09a6\u09cd\u09b0 \u09b8\u09b0\u09a3\u0995\u09be\u09b2\u09c7 \u09ac\u09b2\u09c7\u09b0 \u09ae\u09be\u09a8 \u09aa\u09cd\u09b0\u09be\u09af\u09bc \u09a7\u09cd\u09b0\u09c1\u09ac \u09a5\u09be\u0995\u09c7 \u098f\u09ac\u0982 \u098f\u0987 \u09a7\u09cd\u09b0\u09c1\u09ac \u09ae\u09be\u09a8 F_{1}<\/span>\u0964 \u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u098f\u0987 \u0985\u0982\u09b6\u09c7 \u098f\u0987 \u09ac\u09b2 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09b8\u09ae\u09cd\u09aa\u09a8\u09cd\u09a8 \u0995\u09cd\u09b7\u09c1\u09a6\u09cd\u09b0 \u0995\u09be\u099c, \\Delta W_{1}=F_{1} \\Delta x<\/span><\/p>\r\n\r\n\r\n\r\n

\u0985\u09a8\u09c1\u09b0\u09c2\u09aa\u09ad\u09be\u09ac\u09c7 \u09a6\u09cd\u09ac\u09bf\u09a4\u09c0\u09af\u09bc \u0985\u0982\u09b6\u09c7 x_{i}+\\Delta x<\/span> \u09a5\u09c7\u0995\u09c7 x_{i}+2 \\Delta x<\/span> \u09aa\u09b0\u09cd\u09af\u09a8\u09cd\u09a4 \u0995\u09cd\u09b7\u09c1\u09a6\u09cd\u09b0 \u09b8\u09b0\u09a3 \\Delta x<\/span> \u0964 \u098f\u0987 \u0995\u09cd\u09b7\u09c1\u09a6\u09cd\u09b0 \u09b8\u09b0\u09a3\u0995\u09be\u09b2\u09c7 \u09a7\u09cd\u09b0\u09c1\u09ac \u09ac\u09b2 F_{2}<\/span>\u0964 \u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u09a6\u09cd\u09ac\u09bf\u09a4\u09c0\u09af\u09bc \u0985\u0982\u09b6\u09c7 \u09ac\u09b2 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u0995\u09c3\u09a4 \u0995\u09be\u099c, \\Delta W_{2}=F_{2} \\Delta x<\/span>\u0964 \u09ac\u09b8\u09cd\u09a4\u09c1\u099f\u09bf\u0995\u09c7 x_{i}<\/span> \u09a5\u09c7\u0995\u09c7 x_{f}<\/span> \u09aa\u09b0\u09cd\u09af\u09a8\u09cd\u09a4 \u09b8\u09b0\u09be\u09a4\u09c7 F(x)<\/span> \u09ac\u09b2 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u0995\u09c3\u09a4 \u09ae\u09cb\u099f \u0995\u09be\u099c ,<\/p>\r\n\\begin{aligned}\nW &=\\Delta W_{1}+\\Delta W_{2}+\\Delta W_{3} \\ldots \\ldots+\\Delta W_{N} \\\\\n&=F_{1} \\Delta x+F_{2} \\Delta x+F_{2} \\Delta x \\ldots \\ldots+F_{N} \\Delta x \\\\\n&=\\sum_{K=1}^{N} F_{K} \\Delta x\n\\end{aligned}<\/span>\r\n\r\n\r\n\r\n

\\Delta x<\/span> -\u0995\u09c7 \u09af\u09a4 \u0995\u09cd\u09b7\u09c1\u09a6\u09cd\u09b0 \u09a5\u09c7\u0995\u09c7 \u0995\u09cd\u09b7\u09c1\u09a6\u09cd\u09b0\u09a4\u09b0 \u09a4\u09a5\u09be \\text {N}<\/span>-\u098f\u09b0 \u09ae\u09be\u09a8 \u09af\u09a4 \u09ac\u09c7\u09b6\u09bf \u09b9\u09ac\u09c7 \u09b9\u09bf\u09b8\u09be\u09ac\u0995\u09c3\u09a4 \u0995\u09be\u099c\u09c7\u09b0 \u09ae\u09be\u09a8 \u09a4\u09a4 \u09b8\u09a0\u09bf\u0995 \u09b9\u09ac\u09c7\u0964 \u0986\u09ae\u09b0\u09be \u09ac\u09b2 F(x)<\/span> \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u0995\u09c3\u09a4 \u0995\u09be\u099c\u09c7\u09b0 \u09b8\u09a0\u09bf\u0995 \u09ae\u09be\u09a8 \u09aa\u09c7\u09a4\u09c7 \u09aa\u09be\u09b0\u09bf \u09af\u09a6\u09bf \u09aa\u09b0\u09bf\u09ae\u09be\u09aa\u09c7\u09b0 \u09b8\u09c0\u09ae\u09be\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \\Delta x<\/span> \u0995\u09c7 \u09b6\u09c2\u09a8\u09cd\u09af \u098f\u09ac\u0982 N-\u0995\u09c7 \u0985\u09b8\u09c0\u09ae \u0995\u09b0\u09bf\u0964 \u09a4\u09be\u09b9\u09b2\u09c7 \u09b8\u09a0\u09bf\u0995 \u09ab\u09b2 \u09b9\u09ac\u09c7,<\/p>\r\n\r\n\r\n\r\n\\begin{array}{l}\nW=\\lim _{\\Delta x \\rightarrow 0} \\sum_{K=1}^{N} F_{K} \\Delta x \\\\\n\\Delta x\n\\end{array}<\/span>\r\n

\u0995\u09bf\u09a8\u09cd\u09a4\u09c1 \u0995\u09cd\u09af\u09be\u09b2\u0995\u09c1\u09b2\u09be\u09b8\u09c7\u09b0 \u09ad\u09be\u09b7\u09be\u09df<\/p>\r\n\\lim _{\\Delta x \\rightarrow 0} \\sum_{K=1}^{N} F_{K} \\Delta x<\/span>\r\n

\u09b0\u09be\u09b6\u09bf\u099f\u09bf \u09b9\u099a\u09cd\u099b\u09c7<\/p>\r\n\r\n\r\n\r\n\\int_{x_{i}}^{x_{f}} F(x) d x \\text { \u09af\u09be } x_{i} \\text { \u09a5\u09c7\u0995\u09c7 } x_{f} \\text { \u09aa\u09b0\u09cd\u09af\u09a8\u09cd\u09a4 } x \\text {-\u098f\u09b0 \u09b8\u09ae\u09be\u0995\u09b2\u09a8 (Integration) \u09a8\u09bf\u09b0\u09cd\u09a6\u09c7\u09b6 \u0995\u09b0\u09c7 }<\/span>\r\n\r\n\r\n\r\n

\u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u099f\u09bf \u09a6\u09be\u0981\u09a1\u09bc\u09be\u09af\u09bc,<\/p>\r\nW=\\int_{x_{i}}^{x_{f}} F(x) d x<\/span>\r\n\r\n\r\n\r\n

\u09b8\u0982\u0996\u09cd\u09af\u09be\u0997\u09a4\u09ad\u09be\u09ac\u09c7 \u098f\u0987 \u09b0\u09be\u09b6\u09bf\u099f\u09bf \u09b9\u099a\u09cd\u099b\u09c7 \u09ac\u09b2 \u09ac\u0995\u09cd\u09b0\u09b0\u09c7\u0996\u09be \u098f\u09ac\u0982 x_{i}<\/span> \u0993 x_{f}<\/span> \u09b8\u09c0\u09ae\u09be\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u0985\u09ac\u09b8\u09cd\u09a5\u09bf\u09a4 \\text {x}<\/span> -\u0985\u0995\u09cd\u09b7\u09c7\u09b0 \u0985\u09a8\u09cd\u09a4\u09b0\u09cd\u0997\u09a4 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7\u09b0\u00a0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09ab\u09b2\u0964 \u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u09b8\u09ae\u09be\u0995\u09b2\u09a8\u09c7\u09b0 \u09b8\u09be\u09b9\u09be\u09af\u09cd\u09af\u09c7 \u0995\u09be\u099c \u098f\u09ac\u0982 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09ab\u09b2 \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc \u0995\u09b0\u09be \u09af\u09be\u09af\u09bc\u0964<\/p>\r\n","protected":false},"excerpt":{"rendered":"

\u09aa\u09a6\u09be\u09b0\u09cd\u09a5\u09ac\u09bf\u099c\u09cd\u099e\u09be\u09a8\u09c7 \u0995\u09cd\u09af\u09be\u09b2\u0995\u09c1\u09b2\u09be\u09b8 (Calculus in Physics) \u0995\u09cd\u09af\u09be\u09b2\u0995\u09c1\u09b2\u09be\u09b8 \u09b9\u09b2\u09cb \u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09a8\u09c7\u09b0 \u0997\u09be\u09a3\u09bf\u09a4\u09bf\u0995 \u0985\u09a7\u09cd\u09af\u09af\u09bc\u09a8\u0964 \u098f\u09b0 \u09aa\u09c1\u09b7\u09cd\u099f\u09bf \u09aa\u09cd\u09b0\u09a7\u09be\u09a8 \u09b6\u09be\u0996\u09be \u09b0\u09af\u09bc\u09c7\u099b\u09c7 \u09a1\u09bf\u09ab\u09be\u09b0\u09c7\u09a8\u09b8\u09bf\u09af\u09bc\u09be\u09b2 (Differential) \u0995\u09cd\u09af\u09be\u09b2\u0995\u09c1\u09b2\u09be\u09b8 \u0993 \u0987\u09a8\u09cd\u099f\u09bf\u0997\u09cd\u09b0\u09be\u09b2 (Integral) \u0995\u09cd\u09af\u09be\u09b2\u0995\u09c1\u09b2\u09be\u09b8\u0964 \u09ac\u09bf\u099c\u09cd\u099e\u09be\u09a8\u09c0 \u09a8\u09bf\u0989\u099f\u09a8 \u09b8\u09b0\u09cd\u09ac\u09aa\u09cd\u09b0\u09a5\u09ae \u09aa\u09cd\u09b0\u09be\u09a8\u09cd\u09a4\u09bf\u0995 \u09aa\u09a6\u09be\u09b0\u09cd\u09a5\u09ac\u09bf\u099c\u09cd\u099e\u09be\u09a8\u09c7 \u09a1\u09bf\u09ab\u09be\u09b0\u09c7\u09a8\u09b8\u09bf\u09df\u09be\u09b2 \u0995\u09cd\u09af\u09be\u09b2\u0995\u09c1\u09b2\u09be\u09b8 \u09aa\u09cd\u09b0\u09af\u09bc\u09cb\u0997 \u0995\u09b0\u09c7\u09a8\u0964 \u0997\u09c1\u09b0\u09c1\u09a4\u09cd\u09ac\u0983 \u09aa\u09a6\u09be\u09b0\u09cd\u09a5\u09ac\u09bf\u099c\u09cd\u099e\u09be\u09a8\u09c7 \u0995\u09cd\u09af\u09be\u09b2\u0995\u09c1\u09b2\u09be\u09b8-\u098f\u09b0 \u0985\u09aa\u09b0\u09bf\u09b9\u09be\u09b0\u09cd\u09af \u0997\u09c1\u09b0\u09c1\u09a4\u09cd\u09ac \u09b0\u09af\u09bc\u09c7\u099b\u09c7\u0964 \u0985\u09a8\u09c7\u0995 \u09ac\u09be\u09b8\u09cd\u09a4\u09ac \u09aa\u09cd\u09b0\u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be<\/p>\n

Read More<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[3028,51],"tags":[2507,2510,2509,2508],"_links":{"self":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/42"}],"collection":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/comments?post=42"}],"version-history":[{"count":8,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/42\/revisions"}],"predecessor-version":[{"id":4941,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/42\/revisions\/4941"}],"wp:attachment":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/media?parent=42"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/categories?post=42"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/tags?post=42"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}