Evaluate the iterated integral below. Note that it is necessary to switch the order of integration. $\int _ { 0 } ^ { 1 } \int _ { x } ^ {1 } e^{- 9 y ^ { 2 }} d y d x$
A) $\frac { 1 - e ^ { 9 } } { 9 }$
B) $\frac { 1 - e ^ { - 9 } } { 18 }$
C) $\frac { 1 - e ^ { - 9 } } { 9 }$
D) $\frac { e ^ { - 9 } - 1 } { 18 }$
E) $\frac { 1 - e ^ { - 9 } } { 36 }$

Question

Evaluate the iterated integral below. Note that it is necessary to switch the order of integration. $\int _ { 0 } ^ { 1 } \int _ { x } ^ {1 }  e^{- 9 y ^ { 2 }} d y d x$
A) $\frac { 1 - e ^ { 9 } } { 9 }$
B) $\frac { 1 - e ^ { - 9 } } { 18 }$
C) $\frac { 1 - e ^ { - 9 } } { 9 }$
D) $\frac { e ^ { - 9 } - 1 } { 18 }$
E) $\frac { 1 - e ^ { - 9 } } { 36 }$

Quizplus · Accepted Answer

Switching the order of integration gives $\int_{0}^{1} \int_{0}^{y} e^{-9y^2} dx dy$. Evaluating the inner integral with respect to $x$ gives $y e^{-9y^2}$. Integrating with respect to $y$ from 0 to 1 results in $\frac{1 - e^{-9}}{18}$.

Evaluate the Iterated Integral Below ∫01∫x1e−9y2dydx\int _ { 0 } ^ { 1 } \int _ { x } ^ {1 } e^{- 9 y ^ { 2 }} d y d x∫01​∫x1​e−9y2dydx

Evaluate the Iterated Integral Below $\int _ { 0 } ^ { 1 } \int _ { x } ^ {1 } e^{- 9 y ^ { 2 }} d y d x$