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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}

 

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