Find the area of the solid obtained by rotating the region bounded by the given curves about the specified line.

y=x^3, y=x, x0

Question

Find the area of the solid obtained by rotating the region bounded by the given curves about the specified line.

y=x^3, y=x, x>0

campbell_st · Answer

find the point of intersections of the 2 curves....by equating the curves.... i.e  $$x = x^3$$ or $$x^3 - x =0 $$

which gives  $$x(x^2 -1)=0$$

the points of intersection will be   x = 0 and x = 1     (x = -1 not considered because of initial conditions. 

then the problem is $$V = \pi \int\limits_{0}^{1} (x^3 - x)^2 dx$$

anonymous · Answer

i thought you took the larger radius - the smaller radius. $$(x-x ^{3})$$?

nikvist · Answer

area, not volume !!!

campbell_st · Answer

The area between is rotated.... |dw:1327394267382:dw|

the shape is like the horn of a trumpet 

if in doubt... include absolute value symbols around the integral...