Evaluate the following iterated integral.

Question

Quizplus · Accepted Answer

By performing the integration of the inner integral, we get:
$$\int_{0}^{1} (y^3+1) dx = y^3+y$$

Substituting this in the outer integral, we get:

\begin{align*}
\int_{0}^{2} (y^3+y)(2y-1) dy &= \int_{0}^{2} (2y^4 - y^3 + 2y^2 - y) dy \
&= \left[\frac{2y^5}{5} - \frac{y^4}{4} + \frac{2y^3}{3} - \frac{y^2}{2}ight]_0^2 \
&= \frac{32}{5} - 4 + \frac{16}{3} - 2 \
&= \frac{60}{5} \
&= 12 \
\end{align*}

Therefore, the correct answer is $\boxed{	extbf{(C) }5,955}$.

Evaluate the Following Iterated Integral