Write an equivalent double integral with the order of integration reversed.
-$\int _ { 0 } ^ { 2 } \int _ { 5 x / 2 + 3 } ^ { 8 } d y d x$
A) $\int _ { 2 } ^ { 8 } \int _ { 0 } ^ { 2 ( y - 3 ) / 5 } d x d y$
B) $\int _ { 3 } ^ { 8 } \int _ { 0 } ^ { 2 ( y - 3 ) / 5 } d x d y$
C) $\int _ { 0 } ^ { 8 } \int _ { 0 } ^ { 2 ( y - 3 ) / 5 } d x d y$
D) $\int _ { 3 } ^ { 2 } \int _ { 0 } ^ { 2 ( y - 3 ) / 5 } d x d y$

Question

Quizplus · Accepted Answer

To reverse the order of integration, we need to switch the limits of integration and integrate with respect to $y$ first. The limits of integration for $y$ are from $5x/2 + 3$ to 8 and the limits for $x$ are from 0 to 2. Solving $5x/2 + 3 = y$ for $x$, we get $x = 2(y-3)/5$. Therefore, the equivalent double integral with the order of integration reversed is $\int_{3}^{8}\int_{0}^{2(y-3)/5}dxdy$. The correct choice is $\boxed{	extbf{(B)}}$.

Write an Equivalent Double Integral with the Order of Integration ∫02∫5x/2+38dydx\int _ { 0 } ^ { 2 } \int _ { 5 x / 2 + 3 } ^ { 8 } d y d x∫02​∫5x/2+38​dydx

Write an Equivalent Double Integral with the Order of Integration $\int _ { 0 } ^ { 2 } \int _ { 5 x / 2 + 3 } ^ { 8 } d y d x$