Switching order of integration for ∫∫ e^(-x²) dx dy

[xnitexlitex]

Homework Statement

1 1/2
∫ ∫ e^-x2 dx dy
0 y/2

Homework Equations

***Graph equation***

The Attempt at a Solution

I graphed the function and they made a horizontal strip. However, I can't seem to find the right function with a vertical strip, which is where I'm stuck.

 

[Dick]

Homework Statement

1 1/2
∫ ∫ e^-x2 dx dy
0 y/2

Homework Equations

***Graph equation***

The Attempt at a Solution

I graphed the function and they made a horizontal strip. However, I can't seem to find the right function with a vertical strip, which is where I'm stuck.

The domain of integration is a triangle. Can you describe it?

 

[HallsofIvy]

It might be easier to see if you write the integral
$$\int_{y=0}^{y=1}\int_{x= y/2}^{x= 1/2} e^{-x^2}dx dy$$

Draw the graphs corresponding to the limits of integration.