# Thread: calc question find the volume

1. ## calc question find the volume

How do you setup an integral to compute volume of revolution obtained by rotating the region bounded by curves y=x^2,x=1 and x=2 and the x-axis around the axis y=-1.

2. Originally Posted by harry
How do you setup an integral to compute volume of revolution obtained by rotating the region bounded by curves y=x^2,x=1 and x=2 and the x-axis around the axis y=-1.

There is more than one way to do this. What method are you studying?

3. Originally Posted by harry
How do you setup an integral to compute volume of revolution obtained by rotating the region bounded by curves y=x^2,x=1 and x=2 and the x-axis around the axis y=-1.
Again, someone check me on this. we will use the disk method.

recall, by the disk method, V = int{Area}dx = int{pi*r^2}dx = int{pi*r*f(x)}dx

so we have the radius from the x-axis being x^2, but we are rotating about a line 1 unit from the x-axis, so the radius we will use is 1 + x^2 . the limits as you can see from the diagram are between x= 1 and x = 2. so here goes.

V = int{pi(1 + x^2)^2}dx evaluated between 1 and 2
=> V = pi*int{(1 + x^2)^2}dx
=> V = pi*int{1 + 2x^2 + x^4}dx
=> V = pi[x + (2/3)x^3 + (1/5)x^5] between 1 and 2
=> V = pi[(2 + (2/3)2^3 + (1/5)2^5) - (1 + 2/3 + 1/5)]
=> V = 178pi/15

4. here's a diagram