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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- Mar 31st 2013, 04:27 AMsluggerbrothfind 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

- Mar 31st 2013, 05:02 AMHallsofIvyRe: find exact volume of solid under...HELP!!!!!
Let $\displaystyle x= rcos(\theta)$ and $\displaystyle y= 1+ r sin(\theta)$. Then the hemisphere is given by $\displaystyle z= \sqrt{4- r^2cos^2(\theta)- (1+ rsin(\theta))^2}= \sqrt{5- r^2- 2rsin(\theta)}$ so the volume is

$\displaystyle \int_{r= 0}^1\int_{\theta= 0}^{2\pi}\sqrt{5- r^2- 2rsin(\theta)}d\theta dr$