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Original Question
The region bounded by y= 1/(x^2+2x+5), y=0, x=0, and x=1, is revolved about the x-axis. Find the volume of the resulting solid.Asked by Nycw
The region bounded by y=e^(-x^2),y=0 ,x=0 ,x=1 and is revolved about the y-axis. Find the volume of the resulting solid.
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Answered by
Steve
better use shells for this.
v = ∫[0,1] 2πrh dx
where r = x and h = y = e^(-x^2)
v = π∫[0,1] 2xe^(-x^2) dx
= π(-e^(-x^2)) [0,1]
= π(1 - 1/e)
v = ∫[0,1] 2πrh dx
where r = x and h = y = e^(-x^2)
v = π∫[0,1] 2xe^(-x^2) dx
= π(-e^(-x^2)) [0,1]
= π(1 - 1/e)
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