Thread: Integration by Parts & Volumes of Revolution

For the integration sign I'll use a capital s.

1) Find the volume of revolution when the area between y=(1/x), x=1, x=5, and y=0 is rotated about the x-axis.

V= ((pie) S(1-5) (1/x)^2 dx)
=(pie)(S(1-5))(1/x^2) dx
=(pie)[1/(-3x^3)|(1-5)
=(pie)[(1/((-3)(5)^3) - (1/((-3)(1)^3)]
= -(1126(pie)) / 3

Seems like a wrong answer so if anyone can help thank you.


2) Find the average value of the function of f(x) = (x)^3 + (2)^2 - 5x over [-1,5].

Not sure how to start this one

Oh shoot...my antiderivative is wrong. should be:

1/-x right?

So I got final answer of:

4(pie) / 5