Evaluate the definite integral .
A) 0
B) 1125
C) -1125
D) -2250
E) 2250

Name: Evaluate the definite integral . A) 0 B) 1125 C) -1125 D) -2250 E) 2250
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Question

Evaluate the definite integral  . ​
A) 0 
B) 1125 
C) -1125 
D) -2250 
E) 2250

Quizplus · Accepted Answer

By using the substitution $x = \pi - t$, we have
\begin{align*}
\int_{\pi}^{2\pi} e^{\sin x}\cos x \, dx &= \int_{0}^{\pi} e^{\sin(\pi-t)} \cos(\pi-t) \, dt \
&= \int_{0}^{\pi} e^{-\sin t} \cos t \, dt \
&= -\int_{0}^{\pi} e^{-\sin t} \, d(\cos(t)) \
&= -e^{-\sin t}\bigg|_{0}^{\pi} \
&= -e^0 + e^0 = -1+1 = \boxed{	extbf{(C)} -1125}
\end{align*}

Evaluate the Definite Integral . ​

Evaluate the Definite Integral .