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Homework Statement
Change the Cartesian integral to an equivalent polar integral and evaluate
∫∫dydx
The bounds of the first integral (The outermost) are -5 to 5, and the bounds of the second (inner) are 0 to [itex]\sqrt{ 25-x^{2}}[/itex]
Homework Equations
∫∫dydx == ∫∫r(dr)(d[itex]\Theta[/itex])
[itex]x^{2}[/itex]+[itex]y^{2}[/itex]=[itex]r^{2}[/itex]
x = rCos([itex]\Theta[/itex])
y = rSin([itex]\Theta[/itex])
The Attempt at a Solution
I solved for r by setting y equal to [itex]\sqrt{ 25-x^{2}}[/itex]
after doing this I found r to be 5
I know that typically the next step is to find the bounds for \Theta, but I have no clue as to how to do this, I know how to set up the integral and evaluate it, but I do not know how to determine the bounds for [itex]\Theta[/itex] can anyone please explain that to me?
Thanks for your time.