- #1
Swasse
- 9
- 0
Hey.
∫∫x^3 dxdy, with the area of integration: D={(x,y)∈R^2: 1<=x^2+9y^2<=9, x>=3y}
Did the variable substitution u=x and v=3y so the area of integration became 1<=u^2 + v^2 <=9, u>=v. And the integral became ∫∫(1/3)u^3 dudv. Then I switched to polar coordinates and the integral ∫∫(1/3)r^4cos^3θ drdθ, with 1<=r<=9 and -3/4<=θ<=pi/4.
Any errors so far?
I really appreciate any help you can provide.
Homework Statement
∫∫x^3 dxdy, with the area of integration: D={(x,y)∈R^2: 1<=x^2+9y^2<=9, x>=3y}
The Attempt at a Solution
Did the variable substitution u=x and v=3y so the area of integration became 1<=u^2 + v^2 <=9, u>=v. And the integral became ∫∫(1/3)u^3 dudv. Then I switched to polar coordinates and the integral ∫∫(1/3)r^4cos^3θ drdθ, with 1<=r<=9 and -3/4<=θ<=pi/4.
Any errors so far?
I really appreciate any help you can provide.
Homework Statement
Homework Equations
The Attempt at a Solution
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