Question:
The value of \(\int_0^{\pi/2} \cos x\, e^{\sin x}\,dx\) is
\(\int_0^{\pi/2} \cos x\, e^{\sin x}\,dx\) का मान क्या है?
Options:
- e – 1
- 1
- 0
- -1
- e – 1
- 1
- 0
- -1
Correct Answer: a)
Explanation:
Let \(u = \sin x \implies du = \cos x\,dx\). When \(x = 0, u = 0\); when \(x = \pi/2, u = 1\).
\(\int_0^1 e^u\,du = [e^u]_0^1 = e^1 – e^0 = e – 1\).
\(u = \sin x\) रखने पर: \(\int_0^1 e^u\,du = [e^u]_0^1 = e – 1\)।