# Multiple integral to check

• May 16th 2007, 12:52 PM
totalnewbie
Multiple integral to check
Could somebody check my solution if it is correct.
I don't know if it is right or not.
• May 17th 2007, 12:11 AM
CaptainBlack
Quote:

Originally Posted by totalnewbie
Could somebody check my solution if it is correct.
I don't know if it is right or not.

First observe that the integrand (4-y) is positive on D. Therefore the integral
over D cannot be negative.

The region of integration is 0<x<2, x^2/4<y<1, so our integral may be written:

I = integral_{x=0,2} [integral_{y=x^2/4,1} (4-y) dy] dx

.. = integral_{x=0,2} [7/2 - x^2 + x^4/32] dx

.. = 68/15 = 4.533..

Which agrees with my numerical result using MonteCarlo methods of 4.535.

RonL
• May 17th 2007, 06:09 AM
totalnewbie
Quote:

Originally Posted by CaptainBlack
First observe that the integrand (4-y) is positive on D. Therefore the integral
over D cannot be negative.

The region of integration is 0<x<2, x^2/4<y<1, so our integral may be written:

I = integral_{x=0,2} [integral_{y=x^2/4,1} (4-y) dy] dx

.. = integral_{x=0,2} [7/2 - x^2 + x^4/32] dx

.. = 68/15 = 4.533..

Which agrees with my numerical result using MonteCarlo methods of 4.535.

RonL

Your post came little bit late because I gave my solutions to the teacher today at 10 AM. OK, I will give the correction when the teacher returns my excercise book.
• May 17th 2007, 06:18 AM
CaptainBlack
Quote:

Originally Posted by totalnewbie
Your post came little bit late because I gave my solutions to the teacher today at 10 AM. OK, I will give the correction when the teacher returns my excercise book.

Trying to sort out time zones can be a problem online, you have yours
set up 3 hours east of me, but your ISP appears to be in the Netherlands!?

But to be brief - When was 10 AM? My post is time stamped 08:11 (AM)