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Mathoholic!
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Homework Statement
It is given a set defined as: 0≤x≤1, 0≤y≤1-x. With x,y in ℝ.
f(x,y)=1 (plane parallel to Oxy plane)
They ask you to express the integral ∫∫Setf(x,y)dxdy in polar coordinates and calculate it.
Homework Equations
x=rcosθ
y=rsenθ
r=√x2+y2
The Attempt at a Solution
I've done the variable substitution as:
0≤rcosθ≤1, 0≤rsenθ≤1-cosθ and ∫∫Setrdrdθ
After analysing it for a bit I figured that 0≤r≤1 and that 0≤θ≤[itex]\frac{\pi}{2}[/itex].
However, the solution to the integral is 0.5. For the limits I've established, it gives me [itex]\frac{\pi}{4}[/itex].
I can easily calculate that integral in x,y coordinates but I'm having trouble defining the endpoints of r and θ when changing a set from x,y coordinates to r and θ coordinates.
Can you help me with this?