Calculate the iterated integral. $\int _ { 0 } ^ { x } \int _ { 0 } ^ { 1 } \int _ { 0 } ^ { \sqrt { 1 - y ^ { 2 } } } 4 y \sin x d z d y d x$
A) $\frac { 8 } { 3 }$
B) 4
C) 0
D) $\frac { 3 } { 8 }$
E) None of these

Question

Quizplus · Accepted Answer

The integral evaluates to $\frac{8}{3}$ after performing the integration step by step, starting with $z$, then $y$, and finally $x$.

Calculate the Iterated Integral ∫0x∫01∫01−y24ysin⁡xdzdydx\int _ { 0 } ^ { x } \int _ { 0 } ^ { 1 } \int _ { 0 } ^ { \sqrt { 1 - y ^ { 2 } } } 4 y \sin x d z d y d x∫0x​∫01​∫01−y2​​4ysinxdzdydx

Calculate the Iterated Integral $\int _ { 0 } ^ { x } \int _ { 0 } ^ { 1 } \int _ { 0 } ^ { \sqrt { 1 - y ^ { 2 } } } 4 y \sin x d z d y d x$