If $f(x) = \left\{ \begin{array}{r} e^{\cos x}\sin{x,} \ 2, \end{array}\ \begin{matrix} |x| \leq 2 \ otherwise \end{matrix}, ight.\$ then $\int_{- 2}^{3}{f(x)dx}$ is equal to

Question

If $f(x) = \left\{ \begin{array}{r} e^{\cos x}\sin{x,} \ 2, \end{array}\ \begin{matrix} |x| \leq 2 \ otherwise \end{matrix}, ight.\$ then $\int_{- 2}^{3}{f(x)dx}$ is equal to

Dr. Abubacker · Accepted Answer

(c)
$\int_{- 2}^{3}{f(x)dx = \int_{- 2}^{2}{f(x)dx +}\int_{2}^{3}{f(x)dx}}$
$= \int_{- 2}^{2}{e^{\cos x}\sin{x\ dx +}}\int_{2}^{3}{2\ dx}$
Function of Ist integral is an odd function, therefore the value of Ist integral is zero.
$	herefore\ \ \int_{- 2}^{3}{f(x)dx = 0 + 2\lbrack xbrack_{2}^{3}}$
$= 0 + 2(3 - 2) = 2$

Q. If $f(x) = \left\{ \begin{array}{r} e^{\cos x}\sin{x,} \\ 2, \end{array}\ \begin{matrix} |x| \leq 2 \\ otherwise \end{matrix}, \right.\$ then $\int_{- 2}^{3}{f(x)dx}$ is equal to

Explanation

Reviewed by Dr. Abubacker

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