Reverse the order of integration and then evaluate the integral.
-$$\int _ { 0 } ^ { 70 } \int _ { y / 10 } ^ { 7 } \tan ^ { - 1 } x ^ { 2 } d x d y$$
A) $245 \tan ^ { - 1 } 49 - \frac { 5 } { 2 } \ln 2402$
B) $245 \tan ^ { - 1 } 49 - 5 \ln 2402$
C) $\frac { 245 } { 2 } \tan ^ { - 1 } 49 - 5 \ln 2402$
D) $\frac { 245 } { 2 } \tan ^ { - 1 } 49 - \frac { 5 } { 2 } \ln 2402$

Question

Quizplus · Accepted Answer

The integral's limits change when the order of integration is reversed. Initially, $y$ ranges from $0$ to $70$, and for each $y$, $x$ ranges from $y/10$ to $7$. When the order is reversed, $x$ ranges from $0$ to $7$, and for each $x$, $y$ ranges from $0$ to $10x$. Evaluating the integral with these new limits and simplifying leads to the correct answer, which involves the arctangent of $49$ and the natural logarithm of $2402$, matching the expression in choice A.

Reverse the Order of Integration and Then Evaluate the Integral ∫070∫y/107tan⁡−1x2dxdy\int _ { 0 } ^ { 70 } \int _ { y / 10 } ^ { 7 } \tan ^ { - 1 } x ^ { 2 } d x d y∫070​∫y/107​tan−1x2dxdy

Reverse the Order of Integration and Then Evaluate the Integral $\int _ { 0 } ^ { 70 } \int _ { y / 10 } ^ { 7 } \tan ^ { - 1 } x ^ { 2 } d x d y$