(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show that the area of [tex]x^2/a^2+y^2/b^2=1[/tex] is [tex]\pi ab[/tex]

2. Relevant equations

Given transformations:

[tex]x=au[/tex]

[tex]y=bv [/tex]

3. The attempt at a solution

[tex]J(u,v) = a*b [/tex]

[tex] \int\int ((au)/a)^2+((bv)/b)^2 J(u,v) dudv [/tex]

[tex]\int\int u^2+v^2 J(u,v) dudv [/tex]

[tex]\int_0^{2\pi}\int_0^1 r^2 J(u,v) r drd\theta [/tex]

[tex]\int_0^{2\pi}\int_0^1 a b r^3 drd\theta [/tex]

[tex]\int_0^{2\pi} 1/4 a b d\theta [/tex]

=[tex]\frac{\pi a b}{2}[/tex]

But that's obviously wrong. Where did I mess up?

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# Homework Help: Derivation: Area of Ellipse

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