Optimizing Double Integrals with Base e

[r_swayze]

$$\int_0^1\int_0^y e^{x^2} dx dy$$

The region I am integrating over should look like this graph, right?


I tried switching the bounds but I am left where what I started.

since 0 < x < y, and 0 < y < 1

I can switch to 0 < x < 1 , and x < y < 1

leaving me with the integral $$\int_0^1\int_x^1 e^{x^2} dy dx$$

integrating gives e^x2y

then substituting the values for y gives $$\int_0^1 e^{x^2} - e^{x^2}x dx$$

Am I integrating over the wrong bounds? I know if 0 < y < x, it would work.

 

[LCKurtz]

Everything looks correct and you reversed the limits nicely. I suspect a typo in your textbook. (Of course you can do the second integral but that doesn't help).