Evaluate the double integral integral ∫∫ y dxdy. The plane region is (x-1)^2+(y-1)^2 <=8.

Answer 1

double integral of ydxdy

= integral of y^2/2+ c1 dx

= y^2x/2 +c1x + c2

where c1 and c2 are constants

plane area inside (x-1)^2 +(y-1)^2 =8 is area of a circle with radius sqr8

= pir^2 = 8pi

if you use integral calculus to find the circle's area you should get the same solution