Evaluate the following iterated integral.
A) 5,901
B) 5,931
C) 5,955
D) 5,970
E) 6,017

Question

Evaluate the following iterated integral. 
A) 5,901 
B) 5,931 
C) 5,955 
D) 5,970 
E) 6,017

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