# Calculus, double integral problem

• Apr 6th 2013, 03:27 PM
gfbrd
Calculus, double integral problem
Hey there I need some help with this problem.

Let f be continuous on [a,b] and g continuous on [c,d]. Show that:

Attachment 27833

where R = [a,b] X [c,d]

Please explain each step so that I can understand this problem better thanks!
• Apr 6th 2013, 05:22 PM
chiro
Re: Calculus, double integral problem
Hey gfbrd.

Hint: Try integrating out one of the variables (either x or y) and bring this constant outside the final integral (which will be with respect to the other variable). Once you do this, substitute the old integral in for the constant and you are done.

So as an example Integral Integral f(x)g(y)dxdy = c*Integral g(y)dy. What is c in terms of the integral of f(x)dx?
• Apr 6th 2013, 06:01 PM
gfbrd
Re: Calculus, double integral problem
Edit: hahha nevermind! I figured it out thanks!
• Apr 6th 2013, 06:11 PM
chiro
Re: Calculus, double integral problem
If you integrated out for example f(x)dx over some range you will get F(b) - F(a) as your constant c.