The region between the graphs of x=y2 and x=5y is rotated around the line y=5.

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The region between the graphs of x=y2 and x=5y is rotated around the line y=5

The volume of the resulting solid is
May 1st, 2015

y2? improper syntax. help.

May 1st, 2015

y^2

May 1st, 2015

The first step is to find where x=y^2 and x=5y intersect. One point of intersection is at x=0 and the other is at x=25  (y^2=5y when y=5). Thus we are integrating from x=0 to x=25. We draw a diagram to find our two radii for our "washers". r1 is 5-(sqrtx) and r2 is 5-(1/5x). Using washer method we get pi * integral(0,25) of  -(5-(sqrtx))^2+(5-1/5x)^2  ; integrand is -(25-10sqrtx+x)+(25-2x+1/25x^2) simplifies to -3x+10sqrtx+1/25x^2  . integrating  we get 

-(3/2)x^2+15x^(3/2)+(1/75)x^3 . Evaluating gives -(3/2)*25^2+15*(25)^(3/2)+(1/75)*(25)^3=1145.8333. Multiplying by pi gives 3599.74

May 1st, 2015

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