SATHEE: Definite Integration Question 27

Definite Integration Question 27

Question 27

If $f (x) = \begin{array}{cc} e^{\cos x} \sin x, & for | x | \leq 2 2 & otherwise \end{array}$ then $\int_{- 2}^{3} f (x) d x$ is equal to

$(2000, 2 M)$ (a) 0 (b) 1 (c) 2 (d) 3

Show Answer

Solution:

Given, $f (x) = 2$ , otherwise

$∴ \int_{- 2}^{3} f (x) d x = \int_{- 2}^{2} f (x) d x + \int_{2}^{3} f (x) d x$

$= \int_{- 2}^{2} e^{\cos x} \sin x d x + \int_{2}^{3} 2 d x = 0 + 2 [x]_{2}^{3}$

$[∵ e^{\cos x} \sin x$ is an odd function]

$= 2 [3 - 2] = 2 ∵ \int_{- 2}^{3} f (x) d x = 2$

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