Evaluate the integral.
-$$\int _ { 0 } ^ { \pi / 2 } \theta ^ { 2 } d \theta$$
A) $\frac { \pi ^ { 3 } } { 3 }$
B) $\frac { 8 \pi ^ { 3 } } { 3 }$
C) $\frac { \pi ^ { 3 } } { 24 }$
D) $\frac { 27 \pi ^ { 3 } } { 24 }$

Question

Quizplus · Accepted Answer

We can evaluate the integral using integration by parts:
$$\int \theta ^ { 2 } d \theta= \frac{\theta^3}{3}$$
Using the limits of integration, we have:
$$\int _ { 0 } ^ { \pi / 2 } \theta ^ { 2 } d \theta = \frac { (\pi / 2) ^ { 3 } } { 3 } - \frac { (0) ^ { 3 } } { 3 } = \frac { \pi ^ { 3 } } { 24 }$$
Therefore, the answer is C.

Evaluate the Integral ∫0π/2θ2dθ\int _ { 0 } ^ { \pi / 2 } \theta ^ { 2 } d \theta∫0π/2​θ2dθ

Evaluate the Integral $\int _ { 0 } ^ { \pi / 2 } \theta ^ { 2 } d \theta$