SOLUTION: the region enclosed by the curve wuth equation y=e^2x + 4. the X axis the Y axis and the line X=2 is rotated through 360 degree about the X axis.

Algebra ->  Volume -> SOLUTION: the region enclosed by the curve wuth equation y=e^2x + 4. the X axis the Y axis and the line X=2 is rotated through 360 degree about the X axis.       Log On


   

Question 1082572: the region enclosed by the curve wuth equation y=e^2x + 4. the X axis the Y axis and the line X=2 is rotated through 360 degree about the X axis.

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
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y=e%5E%282x%29%2B4
e%5E%282x%29=y-4
2x=ln%28y-4%29
x=ln%28y-4%29%2F2
and
x=2
So,
A%28y%29=pi%28%282%29%5E2-%28ln%28y-4%29%2F2%29%5E2%29
A%28y%29=pi%284-%28ln%28y-4%29%29%5E2%2F4%29
and
V=int%28%28A%28y%29%29%2Cdy%2Cy=5%2Ce%5E%284%29%2B4%29
V=int%28%28pi%284-%28ln%28y-4%29%29%5E2%2F4%29%29%2Cdy%2Cy=5%2Ce%5E%284%29%2B4%29
V=%281%2F4%29%2814y-%28y-4%29ln%28y-4%29%5E2%2B2%28y-4%29ln%28y-4%29%2B8%29%2BC



V=%281%2F4%29%286%28e%5E4%29%2B64%29-%0D%0A+++++%281%2F4%29%2878%29
V=%281%2F4%29%286%28e%5E4%29-14%29
highlight%28V=%281%2F2%29%283%28e%5E4%29-7%29%29