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 ϕ(x) is continuously differentiable function, then to evaluate integrals of the form ∫ […]
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Here you will learn some integration examples for better understanding of integration concepts. Example 1 : Evaluate : ∫ dx3sinx+4cosx Solution : I = ∫ dx3sinx+4cosx = ∫ dx3[2tanx21+tan2x2]+4[1−tan2x21+tan2x2] = ∫ sec2x2dx4+6tanx2−4tan2x2 let tanx2 =
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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−1x – log|x+√x2–1| + C Where C is the integration constant. i.e. ∫ sec−1x = xsec−1x – \(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−1x + 12 log|1+x2| + C Where C is the integration constant. i.e. ∫
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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−1x – 12 log|1+x2| + C Where C is the integration constant. i.e. ∫
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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−1x – √1–x2 + C Where C is the integration constant. i.e. ∫ cos−1x = xcos−1x
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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−1x + √1–x2 + C Where C is the integration constant. i.e. ∫ sin−1x = xsin−1x
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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. ∫ log x dx
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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|tanx2| + C. where C is the integration constant. i.e. ∫
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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(π4+x2)| + C. where C is the integration constant.
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