- Change the following Cartesian integrals into polar integrals (Hint: draw the region to determine the bounds)
- $\int_{-1}^1 \int_0^{\sqrt{1-x^2}} dy \, dx$
- $\int_{0}^2 \int_0^{\sqrt{4-y^2}} \, (x^2 + y^2) \, dx \, dy$
- $\int_{0}^6 \int_0^y \, x \, dx \, dy$
- Find the area of the region cut from the first quadrant by the cardioid $r=1+\sin \theta$
- Find the area inside one leaf of the rose $r=\cos 3\theta$
- Find the area inside the cardioid $r=1+\cos \theta$ and outside the curve $r=1$.
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