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Math Help - find exact volume of solid under...HELP!!!!!

  1. #1
    Member sluggerbroth's Avatar
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    find exact volume of solid under...HELP!!!!!

    hemisphere z=(4-x^(2)-y^(2))^(1/2) and above region bounded by the graph x^(2)+(y-1)^(2)=1
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  2. #2
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    Re: find exact volume of solid under...HELP!!!!!

    Let x= rcos(\theta) and y= 1+ r sin(\theta). Then the hemisphere is given by z= \sqrt{4- r^2cos^2(\theta)- (1+ rsin(\theta))^2}= \sqrt{5- r^2- 2rsin(\theta)} so the volume is
    \int_{r= 0}^1\int_{\theta= 0}^{2\pi}\sqrt{5- r^2- 2rsin(\theta)}d\theta dr
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