Evaluate double integral of (x^2+y^2)dxdy throughout the area enclosed by n the curves y=4x , x+3=3 , y=0 , y=2
Answer (1)
12th Nov, 2020
Limiting value for x: x+3=3 => x=0 , x= y/4
Limiting value for y : y=0 , y=2
As the limiting value of x is dependent on y then we will integrate with respect to x then with respect to y.
Integrating with respect to x we get => [(x^3/3) + xy^2]
putting the limit of x=y/4 , x=0 we get: [(y^3/192)+(y^3/4)]
Now integrating with respect to y we get: [(1/192)+(1/4)] * (y^4/4)
Putting the limit y=2 , y=0 we get: [(1/192)+(1/4)] *4 => 49/48.
So the answer of the integration is 49/48.
I hope my answer helps you. All the very best for your future endeavors!
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