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posted by  tttt09 on 10/30/2009 2:10:33 AM  |  status: Closed  |  Earned Karma: 25

Polar,Lifesaver!!!

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Using polar coordinates, evaluate the integral which gives the area which lies in the first quadrant between the circles x2+y2=196 and x2−14x+y2=0.
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posted by velixy on 10/30/2009 7:02:31 AM  |  status: Live
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Response Details:
Using polar coordinates, evaluate the integral which gives the area which lies in the first quadrant between the circles x2+y2=142 and x2−14x+y2=0.
polar coordinates
x=14 cos θ
y=14 sin θ   ==> x2+y2=142  ==>  r2 = 142   ==> r=14
x2+y2= 196 and
 x2−14x+y2=0. ==>   x2+y2=14x  r2=142 r cos θ  ==> r= 14 cosθ
r=r
14 = 14 cosθ
cosθ= 1
θ= 0  and θ=2π
A=    Integrate[Integrate[r,{r,14Cos[t],14}],{t,0,2*Pi}]   = 98π
A/4=  98π /4=    49π   /  2 
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