Evaluate the integral.
-$$\int _ { 3 \pi / 2 } ^ { 2 \pi } \theta d \theta$$
A) $\frac { 9 \pi ^ { 2 } } { 8 }$
B) $\frac { 7 \pi ^ { 2 } } { 8 }$
C) $\frac { \pi ^ { 2 } } { 8 }$
D) $\frac { \pi ^ { 2 } } { 2 }$

Question

Quizplus · Accepted Answer

The integral of $\theta$ with respect to $\theta$ is $\frac{1}{2}\theta^2$. Evaluating this from $3\pi/2$ to $2\pi$ gives $\frac{1}{2}(2\pi)^2 - \frac{1}{2}(3\pi/2)^2 = 2\pi^2 - \frac{9\pi^2}{8} = \frac{16\pi^2}{8} - \frac{9\pi^2}{8} = \frac{7\pi^2}{8}$.

Evaluate the Integral ∫3π/22πθdθ\int _ { 3 \pi / 2 } ^ { 2 \pi } \theta d \theta∫3π/22π​θdθ

Evaluate the Integral $\int _ { 3 \pi / 2 } ^ { 2 \pi } \theta d \theta$