Here you will learn what is integration by substitution method class 12 with examples. Let’s begin – Integration By Substitution The method of evaluating an integral by reducing it to standard form by a proper substitution is called integration by substitution. If \(\phi(x)\) is continuously differentiable function, then to evaluate integrals of the form \(\int\) …
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Here you will learn some integration examples for better understanding of integration concepts. Example 1 : Evaluate : \(\int\) \(dx\over {3sinx + 4cosx}\) Solution : I = \(\int\) \(dx\over {3sinx + 4cosx}\) = \(\int\) \(dx\over {3[{2tan{x\over 2}\over {1+tan^2{x\over 2}}}] + 4[{1-tan^2{x\over 2}\over {1+tan^2{x\over 2}}}]}\) = \(\int\) \(sec^2{x\over 2}dx\over {4+6tan{x\over 2}-4tan^2{x\over 2}}\) let \(tan{x\over 2}\) = …
Here you will learn proof of integration of sec inverse x and cosec inverse x. Let’s begin – Integration of Sec Inverse x The integration of sec inverse x or arcsec x is \(xsec^{-1}x\) – \(log|x + \sqrt{x^2 – 1}|\) + C Where C is the integration constant. i.e. \(\int\) \(sec^{-1}x\) = \(xsec^{-1}x\) – \(log|x …
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Here you will learn proof of integration of cot inverse x or arccot x and examples based on it. Let’s begin – Integration of Cot Inverse x The integration of cot inverse x or arccot x is \(xcot^{-1}x\) + \(1\over 2\) \(log |1 + x^2|\) + C Where C is the integration constant. i.e. \(\int\) …
Here you will learn proof of integration of tan inverse x or arctan x and examples based on it. Let’s begin – Integration of Tan Inverse x The integration of tan inverse x or arctan x is \(xtan^{-1}x\) – \(1\over 2\) \(log |1 + x^2|\) + C Where C is the integration constant. i.e. \(\int\) …
Here you will learn proof of integration of cos inverse x or arccos x and examples based on it. Let’s begin – Integration of Cos Inverse x The integration of cos inverse x or arccos x is \(xcos^{-1}x\) – \(\sqrt{1 – x^2}\) + C Where C is the integration constant. i.e. \(\int\) \(cos^{-1}x\) = \(xcos^{-1}x\) …
Here you will learn proof of integration of sin inverse x or arcsin x and examples based on it. Let’s begin – Integration of Sin Inverse x The integration of sin inverse x or arcsin x is \(xsin^{-1}x\) + \(\sqrt{1 – x^2}\) + C Where C is the integration constant. i.e. \(\int\) \(sin^{-1}x\) = \(xsin^{-1}x\) …
Here you will learn what is the integration of log x dx with respect to x and examples based on it. Let’s begin – Integration of Log x The integration of log x with respect to x is x(log x) – x + C. where C is the integration Constant. i.e. \(\int\) log x dx …
Here you will learn proof of integration of cosecx or cosec x and examples based on it. Let’s begin – Integration of Cosecx or Cosec x The integration of cosec x is log |cosec x – cot x| + C or \(log |tan {x\over 2}|\) + C. where C is the integration constant. i.e. \(\int\) …
Here you will learn proof of integration of secx or sec x and examples based on it. Let’s begin – Integration of Secx or Sec x The integration of sec x is log |sec x + tan x| + C or \(log |tan ({\pi\over 4} + {x\over 2})|\) + C. where C is the integration constant. …
