Homework Statement
\int_0^∞ x^2exp(-x/2) dx
Homework Equations
The Attempt at a Solution
Using u substitution:
u = x/2
du = 1/2 dx
\int_0^∞ 4u^2exp(-u) du*2
= 8 \Gamma(3)
= 8*3!
= 48
But the correct answer is 16 when I plug it in Wolfram's definite integral...
Just noticed the SAME question was asked 3 days ago.
https://www.physicsforums.com/showthread.php?t=554227&highlight=change+the+order+of+integration
@HallsofIvy, I came up with the same solution as you for dxdydz. However, when I integrate for f(x,y,z) = 1, the answer is incorrect. I do not...
Homework Statement
\int^{1}_{0}\int^{x^2}_{0}\int^{y}_{0} f(x,y,z) dz dy dx
Find 5 equivalent iterated integrals.
Homework Equations
0 ≤ z ≤ y
0 ≤ y ≤ x^2
0 ≤ x ≤ 1
The Attempt at a Solution
1) \int^{1}_{0}\int^{√y}_{0}\int^{x^2}_{0} f(x,y,z) dz dx dy
I will try...