JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

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Application +4 | -1

Let

{I_n} = \int {{{\tan }^n}\,x\,dx\left( {n > 1} \right)}

. If

{I_4} + {I_6} = a\,{\tan ^5}x + b{x^5} + C

, where

C

is a constant of integration, then the ordered pair

(a,\,b)

is equal to

View answer and explanation

Correct option: B

\left( {\frac{1}{5},0} \right)

Option B

\left( {\frac{1}{5},0} \right)

is correct because by using the reduction formula for the integral of tan^n(x), we can find the values of a and b.

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\int \sin ^5 x \cos ^4 x d x=

f(x)

\int\limits_{0}^{t^2} x f(x) d x=\frac{2}{5} t^5

f\left(\frac{4}{25}\right)

\int \frac{1-7 \cos ^2 x}{\sin ^7 x \cos ^2 x} d x=\frac{f(x)}{\sin ^7 x}+C

\int {e}^{{x}^2}\left(2-\frac{1}{{x}^2}\right) {de}={e}^{{x}^2} {f}({x})+{C}

{f}\left(\frac{1}{2}\right)=2

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{C}

\int \frac{x^7}{\left(1-x^2\right)^5} d x

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