SOLUTION: Find (x,y) position of centroid of the area under curve y=e^(-x) from x=0 to x=1.assume e=2.718

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Question 859029: Find (x,y) position of centroid of the area under curve y=e^(-x) from x=0 to x=1.assume e=2.718
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
First find the area.
A=int%28e%5E%28-x%29%2Cdx%2C0%2C1%29=-e%5E%28-x%29%2BC=%28e-1%29%2Fe=0.632
Now,
x%5Bc%5D%2AA=int%28xe%5E%28-x%29%2Cdx%2C0%2C1%29
x%5Bc%5D%2AA=-e%5E%28-x%29%28x%2B1%29%2BC
x%5Bc%5D%2AA=%28e-2%29%2Fe
x%5Bc%5D%2A0.632=0.264
x%5Bc%5D=0.418
.
.
y%5Bc%5D%2AA=%281%2F2%29%2Aint%28%28e%5E%28-x%29%29%5E2%2Cdx%2C0%2C1%29
y%5Bc%5D%2AA=%281%2F2%29%2A%28-%281%2F2%29%28e%5E%28-2x%29%29%29%2BC
y%5Bc%5D%2AA=%281%2F4%29%28%28e%5E2-1%29%2Fe%5E2%29
y%5Bc%5D%2A0.632=0.216
y%5Bc%5D=0.342