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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 ∫∫

_{Set}f(x,y)dxdy in polar coordinates and calculate it.

## Homework Equations

x=rcosθ

y=rsenθ

r=√x

^{2}+y

^{2}

## The Attempt at a Solution

I've done the variable substitution as:

0≤rcosθ≤1, 0≤rsenθ≤1-cosθ and ∫∫

_{Set}rdrdθ

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?