Write an equivalent double integral with the order of integration reversed.
-$$\int _ { 3 } ^ { 7 } \int _ { 10 - x } ^ { 7 } d y d x$$
A) $\int _ { 3 } ^ { 4 } \int _ { 10 - y } ^ { 7 } d x d y$
B) $\int _ { 3 } ^ { 7 } \int _ { 10 - y } ^ { 7 } d x d y$
C) $\int _ { 3 } ^ { 7 } \int _ { 7 - y } ^ { 4 } d x d y$
D) $\int _ { 3 } ^ { 4 } \int _ { 7 - y } ^ { 4 } d x d y$

Question

Quizplus · Accepted Answer

To reverse the order of integration, we need to switch the order of the limits of integration and the order of the differentials. So the equivalent double integral with the order of integration reversed is:
$$\int_{10-y}^{7} \int_{3}^{7-y} dx dy$$
This gives us option B as the correct answer.

Write an Equivalent Double Integral with the Order of Integration ∫37∫10−x7dydx\int _ { 3 } ^ { 7 } \int _ { 10 - x } ^ { 7 } d y d x∫37​∫10−x7​dydx

Write an Equivalent Double Integral with the Order of Integration $\int _ { 3 } ^ { 7 } \int _ { 10 - x } ^ { 7 } d y d x$