Parametric Equations and integrals that represent volumes

peterpam89
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Homework Statement



A surface S is formed by rotating a quarter ellipse C about the X-axis. Write an integral that represents the volume enclosed by S. the ellipse is represented by two points, (2,1) at which t= pi/2, and (4,0) at which t=0.

Homework Equations



Ellipse w/radii a,b, in x,y: x= x subscript 0 + a cos (t), y = y subscript 0 + b sin (t)
Cartesian equation of ellipse.

The Attempt at a Solution



Eek. I don't really know where to even start with this problem... any ideas?
 
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You could try x(t)=2+2*cost and y(t)=sint
 

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There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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