Reverse the order of integration and then evaluate the integral.
-$$\int _ { 0 } ^ { 42 } \int _ { y / 7 } ^ { 6 } e ^ { x ^ { 2 } } d x d y$$
A) $\frac { 7 } { 2 } \left( e ^ { 36 } - 1 \right)$
B) $\frac { 7 } { 4 } \mathrm { e } ^ { 36 }$
C) $\frac { 7 } { 4 } \left( \mathrm { e } ^ { 36 } - 1 \right)$
D) $\frac { 7 } { 2 } \mathrm { e } ^ { 36 }$

Question

Quizplus · Accepted Answer

The limits for x are from y/7 to 6, and for y from 0 to 42. Reversing gives x from 0 to 6 and y from 7x to 42. Evaluating the integral gives $\frac { 7 } { 2 } \left( e ^ { 36 } - 1 \right)$.

Reverse the Order of Integration and Then Evaluate the Integral ∫042∫y/76ex2dxdy\int _ { 0 } ^ { 42 } \int _ { y / 7 } ^ { 6 } e ^ { x ^ { 2 } } d x d y∫042​∫y/76​ex2dxdy

Reverse the Order of Integration and Then Evaluate the Integral $\int _ { 0 } ^ { 42 } \int _ { y / 7 } ^ { 6 } e ^ { x ^ { 2 } } d x d y$