If f(x) = begin{cases} e^{cos x} sin x, & tex | vedclass

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(B) We need to evaluate the integral $\int_{-2}^{3} f(x) dx$.Split the integral based on the definition of $f(x)$:$\int_{-2}^{3} f(x) dx = \int_{-2}^{

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$2$

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(B) We need to evaluate the integral $\int_{-2}^{3} f(x) dx$.Split the integral based on the definition of $f(x)$:$\int_{-2}^{3} f(x) dx = \int_{-2}^{2} f(x) dx + \int_{2}^{3} f(x) dx$For $|x| \leq 2$,$f(x) = e^{\cos x} \sin x$. Note that $g(x) = e^{\cos x} \sin x$ is an odd function because $g(-x) = e^{\cos(-x)} \sin(-x) = e^{\cos x} (-\sin x) = -g(x)$.The integral of an odd function over a symmetric interval $[-a, a]$ is $0$. Thus,$\int_{-2}^{2} e^{\cos x} \sin x dx = 0$.For $x > 2$,$f(x) = 2$. Therefore,$\int_{2}^{3} 2 dx = 2[x]_{2}^{3} = 2(3 - 2) = 2(1) = 2$.Adding these results,we get $0 + 2 = 2$.

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

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