Indicate the method you use to set up the integrals (do not integrate) that give the volume of the solid generated by rotating the region R around:(adsbygoogle = window.adsbygoogle || []).push({});

The region R is bounded by the curves y=x, x= 2-y^2 and y=0

i.) the x-axis

ii.) the y-axis

iii.) the line x= -2

iv.) the line y= 1

work shown:

y=x ,

x= 2- y^2

y= sqrt(2-x)

i.) integral of Pi*[(x)- (sqrt(2-x))] dx as x goes from 0 to 1

ii.) integral of 2*Pi*x*[(x)-sqrt(2-x)]dx as y goes from 0 to 1

iii.) integral of 2*Pi*(-2-x)*[(x)-(sqrt(2-x))]dx as x goes from 0 to 1

iv.) integral of Pi*[(x-1)-(sqrt(2-x-1)]dx as y goes from 0 to 1

I think my definite integral limits are wrong... and in general my integral setup is wrong.. please help

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Volume of the solid region with respect to x,y-axises, and lines x and y work shown

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