CostasDBD
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1. Was wondering if anyone could help me confirm the polar limits of integration for the below double integral problem. The question itself is straight forward in cartesian coordinates, but in polar form, I'm a bit suspect of my theta limits after having sketched the it out. any help much appreciated.
2. Homework Equations
[tex]\int^{6}_{0}\int^{y}_{0}xdxdy[/tex]
in polar form:
[tex]\int^{\frac{\pi}{2}}_{\frac{\pi}{4}}\int^{6cosec\theta}_{0} r^{2}cos\theta dr d\theta[/tex]
Using a trig substitution over pi/2 and pi/4, i get an answer of 36. it's just when i sketch it, i get a triangle which only has half that area. am i missing something obvious? cheers
2. Homework Equations
[tex]\int^{6}_{0}\int^{y}_{0}xdxdy[/tex]
in polar form:
[tex]\int^{\frac{\pi}{2}}_{\frac{\pi}{4}}\int^{6cosec\theta}_{0} r^{2}cos\theta dr d\theta[/tex]
The Attempt at a Solution
Using a trig substitution over pi/2 and pi/4, i get an answer of 36. it's just when i sketch it, i get a triangle which only has half that area. am i missing something obvious? cheers
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