Definite Integration Question 27
Question 27
- If $f(x)=\begin{array}{cc}e^{\cos x} \sin x, & \text { for }|x| \leq 2 \ 2 & \text { otherwise }\end{array}$ then $\int_{-2}^{3} f(x) d x$ is equal to
$(2000,2 M)$ (a) 0 (b) 1 (c) 2 (d) 3
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Solution:
- Given, $f(x)=2$, otherwise
$\therefore \int_{-2}^{3} f(x) d x=\int_{-2}^{2} f(x) d x+\int_{2}^{3} f(x) d x$
$$ =\int_{-2}^{2} e^{\cos x} \sin x d x+\int_{2}^{3} 2 d x=0+2[x]_{2}^{3} $$
$\left[\because e^{\cos x} \sin x\right.$ is an odd function]
$$ =2[3-2]=2 \quad \because \int_{-2}^{3} f(x) d x=2 $$
