y = x^2
y = 2x
What is the volume of the region bounded by y = x^2 and y = 2x around y = 3?
I guess the basics steps for solving this would be:
find the area of the half-ellipse [formed by y=x^2 around y=3] = 4/3 abc
then subtract the area of the internal cone formed by the revolution of y=2x from the point of origin following the radius of x=3/2.
so the area of the cone is 1/3 (1.5)^2(3) = 2.25
now just find the area of the half-ellipse formed by y=x^2 revolved around the y axis with a bound at {y=0 and y=3}.
then subtract:
Area of half an Ellipse - 2.25
Area of the Ellipse = (4/3) (1.73)(3)(1.73) = ((4/3)(9) )/2 <--- remember its only half a ellipse
so the answer is 6 - 2.25 = 3.75 ... i think.. O and don't forget to include unit^3 in there.