Q62 / 100 · BITSAT 2023 (Memory Based Paper 2) · Mathematics
$\int_0^{\pi / 4} \cos x e^{\sin x} d x$ is equal to
- A$e+1$
- Correct answerB$e-1$
- C$e$
- D$-e$
Solution
Suppose, $I=\int_0^{\pi / 2} \cos x e^{\sin x} d x$
Let $\sin x=t \Rightarrow \cos x d x=d t$
$x \rightarrow 0 \Rightarrow t \rightarrow 0$
and $x \rightarrow \frac{\pi}{2} \Rightarrow t \rightarrow 1$
So $I=\int_0^1 e^t d t=\left[e^t\right]_0^1=e-1$
Let $\sin x=t \Rightarrow \cos x d x=d t$
$x \rightarrow 0 \Rightarrow t \rightarrow 0$
and $x \rightarrow \frac{\pi}{2} \Rightarrow t \rightarrow 1$
So $I=\int_0^1 e^t d t=\left[e^t\right]_0^1=e-1$
Hence, the correct answer is option: 'B'.