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Problem with double integral

Posted 9 years ago

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.

enter image description here

where a=1.5

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

POSTED BY: M K
3 Replies
Posted 9 years ago
In[1]:= Integrate[Integrate[x^5 E^(y^2), {y, x^2, 2.25}], {x, 0, 1.5}]

Out[1]= 53.5678
POSTED BY: Imran Khan

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

http://www.wolframalpha.com/input/?i=Integrate+E%5E%28y%5E2%29+with+respect+to+y

POSTED BY: Sean Clarke
Posted 9 years ago
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
POSTED BY: Erik Mahieu
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