Consider the integral $\int _ { 1 } ^ { 5 } \int _ { 9 x } ^ { 45 } f ( x , y ) d y d x$ Rewrite the integral with the integration performed in the opposite order.
A) $\int _ { 9 x } ^ { A 5 } \int _ { 1 } ^ { y / 9 } f ( x , y ) d x d y$
B) $\int _ { 9 } ^ { 4 5 } \int _ { 1 } ^ { y / 9 } f ( x , y ) d y d x$
C) $\int _ { 9 } ^ { 4 5 } \int _ { 1 } ^ { y / 9 } f ( x , y ) d x d y$
D) $\int _ { 9 } ^ { 45 } \int _ { 1 } ^ { 0 y } f ( x , y ) d x d y$

Question

Quizplus · Accepted Answer

To switch the order of integration, we first identify the bounds for $y$ and $x$ in the original integral. The original bounds are $1 \leq x \leq 5$ and $9x \leq y \leq 45$. When reversing the order, $y$ ranges from $9$ to $45$, and for each $y$, $x$ starts from $1$ and goes up to $y/9$, which matches option C.

Consider the Integral ∫15∫9x45f(x,y)dydx\int _ { 1 } ^ { 5 } \int _ { 9 x } ^ { 45 } f ( x , y ) d y d x∫15​∫9x45​f(x,y)dydx

Consider the Integral $\int _ { 1 } ^ { 5 } \int _ { 9 x } ^ { 45 } f ( x , y ) d y d x$