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  • Explain solution RD Sharma class 12 chapter 19 Definite Integrals exercise Multiple choice question 20 maths

Explain solution RD Sharma class 12 chapter 19 Definite Integrals exercise Multiple choice question 20 maths

Answers (1)

best_answer

Answer:

e-1

Given:

\int_{0}^{\frac{\pi}{2}} \cos x \cdot e^{\sin x} d x

Hint:

You must know about \frac{d}{d x}(\sin x) and \int e^{t} d t
 

Explanation:  

Let

I=\int_{0}^{\frac{\pi}{2}} \cos x \cdot e^{\sin x} d x

Put

\begin{aligned} &\sin x=t \\\\ &\cos x \; d x=d t \end{aligned}

 Whenx=0 then t= 0

When x=\frac{\pi }{2}  then t=1

\begin{aligned} &=\int_{0}^{1} e^{t} d x \\\\ &=\left[e^{t}\right]_{0}^{1} \\\\ &=e^{1}-e^{0} \\\\ &=e-1 \end{aligned}

 

Posted by

infoexpert26

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