# range

• Mar 21st 2010, 09:15 AM
alexandrabel90
range
given that f(x,y) =30xy^2 for x-1<y<1-x and 0<x<1. find F(0.5,0.5)

i know that we need to do double integration and i tried to integration from -0.5 to (1-x) dy followed by integration from 0 to 0.5 dx..but my answer was wrong...

may i know what is wrong with my understanding of this question?

thanks!
• Mar 21st 2010, 11:36 PM
CaptainBlack
Quote:

Originally Posted by alexandrabel90
given that f(x,y) =30xy^2 for x-1<y<1-x and 0<x<1. find F(0.5,0.5)

i know that we need to do double integration and i tried to integration from -0.5 to (1-x) dy followed by integration from 0 to 0.5 dx..but my answer was wrong...

may i know what is wrong with my understanding of this question?

thanks!

$\displaystyle \int_{x=0}^{0.5} \int_{y=x-1}^{0.5} f(x,y)\; dydx$

CB
• Mar 22nd 2010, 12:48 AM
alexandrabel90
how do you decide that tHe lower limitt for y is x-1 and not jusT -1?does the first integration usually involve a variable?

sorry im new to this chapter so im still nt sure how im suppose to find the limts.
thanks.
• Mar 22nd 2010, 01:51 AM
CaptainBlack
Quote:

Originally Posted by alexandrabel90
how do you decide that tHe lower limitt for y is x-1 and not jusT -1?does the first integration usually involve a variable?

sorry im new to this chapter so im still nt sure how im suppose to find the limts.
thanks.

The range of y is specified in terms of x so y should be the inner integral, leaving x as the outer integral.

CB
• Mar 27th 2010, 05:46 AM
alexandrabel90
if i want to find F(o.5,2)

would the double integral be from x-1 to 1-x for dy and then followed by x=0 to 0.5 for dx?

thanks!