Question

Can you help me with this double integral?

`int_0^1int_(3y)^3e^(x^2)dxdy`

Answer 1

Similar to your previous question, change the order of integration.

Explanation:

We have `x` bounded by `x=3y` (which is also `y = 1/3x`) and by `x=3`.

Graph those lines:

We need `3y <=x<=3` and also `0<=y<=1`, so the region over which we are integrating looks like:

To change the order of integration, we'll need limits of integrating for

`int int e^(x^2) \ dy \ dx`

`y` goes from `0` to the line `y=1/3x` and `x` goes from `0` to `3`.

So we need to evaluate

`int_0^3 int_0^(1/3x) e^(x^2) \ dy \ dx`