# Thread: Weird integral on assignment

1. ## Weird integral on assignment

this integral appeared on an online assignment, but im really having troubles figuring out the domain region D on this. I could simply use the upper and lower limits to sketch the domain D. However, the '7y' component is ticking me off, why cant dy vary from 7x to 7 for example??? i need to know this because i need to reverse the order of integration to dydx and to do so, i need to learn how to set up the limits for the new iteration.

2. Isn't it as simple as

$I=\int_0^1\int_{7y}^7 e^{x^2}dxdy$
$I=\int_0^1 \left[2xe^{x^2}\right]_{7y}^7dy$
$I=\int_0^1 14e^{49}-14ye^{49y^2}dy$

?

3. Hello, ramzouzy!

$\int^1_0 \int^7_{7y} e^{x^2}\,dx\,dy$

The limits are: . $\begin{array}{ccc}y\:=\:1 & & x \:=\:7 \\ y\:=\:0 & & x \:=\:7y \end{array}$

The region looks like this:
Code:
        |
1|               * (7,1)
|           *:::|
|       *:::::::|
|   *:::::::::::|
- - * - - - - - - - + - -
|               7

Reversing the order, we have: . $\int^7_0 \int^{\frac{x}{7}}_0 e^{x^2}\,dy\,dx$

Can you finish it?