Hey guys, really need help with a Volumes question.
The volume enclosed between the curves y = x^4 and y = x^3 is rotated about the y-axis. Find the volume swept out using cylindrical shells
I'm getting a negative answer for some reason...
I'm doing Volume of y=x^4 revolved minus the volume of y=x^3 revolved.
delta(V) = 2*pi*r*h*delta(r).
For y=x^4, r = x, h = x^4, so V = Integral from 0 to 1 of 2*pi*x^5
For y=x^4, r = x, h = x^3, V = Integral from 0 to 1 of 2*pi*x^4
Volume of region enclosed = Integral from 0 to 1 of [2*pi*x^5 - 2*pi*x^4]
I'm getting a negative number

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where do x^4 and x^3 match up? 0 and 1 right?

try again:
2pi {S} x(x^4) - x(x^3) dx ; [0,1]

x^5 ints to x^6/6 and x^4 ints up to x^5/5

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