Find the volume of the solid obtained by rotating the region under the graph of the function f(x)=2x+1 about the x-axis over the interval [0,1]. I have no clue how to start this..... :(

Answer 1

For you to say that you have no clue how to start this straightforward question is not a good sign if you are in a Calculus course.

by Calculus, take vertical discs of width dx and height 2x+1
V = π ∫ r^2 dx

V = π∫(2x+1)^2 dx from 0 to 1
= π [ (1/6)(2x+1)^3 ] from 0 to 1
= π ((1/6)(27) - (1/6)(1^3) )
= π ( 27/6 - 1/6)
= 13π/3