The iterated integral $\int _ { 0 } ^ { \frac { \pi } { 4 } } \left[ \int _ { 0 } ^ { 1 } 2 x \cos ( y ) d x \right] d y$ is

A) $\frac { 1 } { \sqrt { 3 } }$
B) $\frac { 1 } { 2 }$
C) $\frac { 1 } { 3 }$
D) $\frac { 1 } { 5 }$
E) $\frac { 1 } { \sqrt { 2 } }$

Question

The iterated integral $\int _ { 0 } ^ { \frac { \pi } { 4 } } \left[ \int _ { 0 } ^ { 1 } 2 x \cos ( y ) d x \right] d y$ is

A) $\frac { 1 } { \sqrt { 3 } }$
B) $\frac { 1 } { 2 }$
C) $\frac { 1 } { 3 }$
D) $\frac { 1 } { 5 }$
E) $\frac { 1 } { \sqrt { 2 } }$

Quizplus · Accepted Answer

The Answer is E

The Iterated Integral ∫0π4[∫012xcos⁡(y)dx]dy\int _ { 0 } ^ { \frac { \pi } { 4 } } \left[ \int _ { 0 } ^ { 1 } 2 x \cos ( y ) d x \right] d y∫04π​​[∫01​2xcos(y)dx]dy