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  • Explain solution RD Sharma class 12 chapter 19 Definite Integrals exercise Multiple choice question 46 maths

Explain solution RD Sharma class 12 chapter 19 Definite Integrals exercise Multiple choice question 46 maths

Answers (1)

Answer:

1

Hint:

To solve this question we have to use substitution method.

Given:

\int_{0}^{1} \tan \left(\sin ^{-1} x\right) d x

Explanation:

\begin{aligned} &\sin ^{-1} x=t \\\\ &x=\sin t \\\\ &d x=\cos t d t \\\\ &\text { When } x=0, \sin ^{-1} 0=0 \\\\ &\text { When } x=1, \sin ^{-1} 1=\frac{\pi}{2} \end{aligned}

\begin{aligned} &I=\int_{0}^{\frac{\pi}{2}} \tan t \cdot \cos t \; d t \\\\ &\frac{\sin t}{\cos t}=\tan t \\\\ &\sin t=\cos t \cdot \cos t \end{aligned}

\begin{aligned} &=\int_{0}^{\frac{\pi}{2}} \sin t d t \\\\ &I=[-\cos t]_{0}^{\frac{\pi}{2}} \\\\ &I=0-(-1) \\\\ &=1 \end{aligned}

 

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