# Thread: Multiple integral to check

1. ## Multiple integral to check

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

2. 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

3. 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.

4. 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)