Problem with double integral

Questions
,
1

Hello,
I have problem with following integral, not sure which method am I supposed to use to solve it.
I hope someone will get an idea for it, since even Wolframalpha doesn’t help much.

integral.jpeg.png

where a=1.5

P.S. I hope I did choose the right group for post, first time posting here
Thanks in advance!

2

In[3]:= With[{a = 1.5},
Integrate[Integrate[x^5 Exp[y^2], {y, x^2, a^2}], {x, 0, a}]]

Out[3]= 53.5678

Or, via a general symbolic solution:

In[5]:= Integrate[Integrate[x^5 Exp[y^2], {y, x^2, a^2}], {x, 0, a}]
% /. a -> 1.5

Out[5]= 1/12 (1 + (-1 + a^4) E^a^4)

Out[6]= 53.5678
3

Evaluate the inner integral with Wolfram|Alpha. What happens when you do that?

4

In[1]:= Integrate[Integrate[x^5 E^(y^2), {y, x^2, 2.25}], {x, 0, 1.5}]

Out[1]= 53.5678