Evaluate the integral.
-$$\int _ { 0 } ^ { \pi } \theta ^ { 2 } \mathrm {~d} \theta$$
A) $\frac { \pi ^ { 3 } } { 3 }$
B) $\frac { 19 \pi ^ { 3 } } { 24 }$
C) $\frac { 27 \pi ^ { 3 } } { 24 }$
D) $\frac { 8 \pi ^ { 3 } } { 3 }$

Question

Quizplus · Accepted Answer

The integral of $\theta^2$ with respect to $\theta$ is $\frac{\theta^3}{3}$. Evaluating this from $0$ to $\pi$, we get $\frac{\pi^3}{3} - \frac{0^3}{3} = \frac{\pi^3}{3}$.

Evaluate the Integral ∫0πθ2 dθ\int _ { 0 } ^ { \pi } \theta ^ { 2 } \mathrm {~d} \theta∫0π​θ2 dθ

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