SOLUTION: Please help me with this problem: determine the are between the graph of y = {{{xe^(-x^2)}}} and the x axis over the interval [0,1]. (the function is nonnegative over this interv

Algebra ->  Finance -> SOLUTION: Please help me with this problem: determine the are between the graph of y = {{{xe^(-x^2)}}} and the x axis over the interval [0,1]. (the function is nonnegative over this interv      Log On


   

Question 1031666: Please help me with this problem:
determine the are between the graph of y = xe%5E%28-x%5E2%29 and the x axis over the interval [0,1]. (the function is nonnegative over this interval.)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Integrate,
A=int%28%28xe%5E%28-x%5E2%29%29%2Cdx%2C0%2C1%29
Substitute,
u=e%5E%28-x%5E2%29
du=e%5E%28-x%5E2%29%2A%28-2xdx%29
xe%5E%28-x%5E2%29dx=-du%2F2
So,
A=int%28%28-1%2F2%29%2Cdu%2C0%2C1%29
A=-u%2BC%29
A=-e%5E%28-x%5E2%29%2F2%2BC
A=%28e%5E%280%29-e%5E%28-1%29%29%2F2
A=1-1%2F%282e%29
highlight%28A=%28e-1%29%2F%282e%29%29