Question
Explain what is wrong with the statement. If $R$ is the region bounded by $x=1, y=0, y=x,$ then in polar coordinates $\int_{R} x d A=\int_{0}^{\pi / 4} \int_{0}^{1} r^{2} \cos \theta d r d \theta$.
Step 1
In polar coordinates, $x = r \cos \theta$ and $dA = r dr d\theta$. So, the integral $\int_{R} x d A$ becomes $\int_{R} r \cos \theta \cdot r dr d\theta$. Show more…
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