# Thread: Area of solid formed by rotating in about the x axis

1. ## Area of solid formed by rotating in about the x axis

A region is bounded by the lines y=√x,y=0 and y=x-2. Find the volume of the solid by rotating it about the x axis.

what do i do?

2. Before I explain my steps, is the correct answer known to you? If so, what is it?

3. its a multiple choice

it's either

8pi/3
16pi/3
20pi/3
24pi/3
or
32pi/3

this text book doesnt have answers

4. Ok, so the answer is 8pi/3.

You must first draw the graph of the functions, y=rt.x, y=0 and y=x-2, so you know where the area bounded by the curves is above and below the x-axis.

The formula for the volume is pi (integral sign) (f(x))^2 - (g(x))^2 dx.
Your f(x) function is always your bigger function, so rt.x and so g(x) is x-2. Integrate that and you get: pi [(-x^3/3 + 5x^2/2 -4x).

From your graph you know that your lower limit is 0 and your upper limit is 4.

Sub. in x=0 into the anti-derivative from above and subtract is from the value you get when you sub in x=4 into the anti-derivative.