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?
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.
The answer you get should be 8pi/3, which is the answer.
Earlier, I mentioned to graph so you can see where the area is above and below, the area above and below cancels out here so 8pi/3 is the final answer.