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## anonymous 5 years ago 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

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1. campbell_st

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 $V = \pi \int\limits_{0}^{1} (x^3 - x)^2 dx$

2. anonymous

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

3. nikvist

area, not volume !!!

4. campbell_st

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...

5. nikvist

rotation about line y=x

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