Question
The value of $\int\limits^\frac{\pi}{4}_0\cos\text{x}\text{ e}^{\sin\text{x}}\text{ dx}$ is:
- 1
- e - 1
- 0
- 1
Solution:
Let, $\text{I}=\int\limits^\frac{\pi}{4}_0\cos\text{x}\text{ e}^{\sin\text{x}}\text{dx}$
Let $\sin\text{x}=\text{t},$ then $\cos\text{x}\text{ dx}=\text{dt}$
when $\text{x}=0,\text{t}=0$ and $\text{x}=\frac{\pi}{2},\text{t}=1$
Therefore the integrel becomes
$\text{I}=\int\limits^1_0\text{e}^\text{t}\text{dt}$
$=\big[\text{e}^\text{t}\big]^1_0$
$=\text{e}-1$
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