We can see from the picture that the limits of integration go from to . We slice the region into tiny slices and pretend the slice at angle θ is a slice of a perfect circle with radius *r* = sinθ + 1
for that particular value of θ. The area of the entire perfect circle is π(sinθ + 1)^{2} and the area of the tiny slice is a fraction of that: Adding up the areas of the tiny slices and letting the number of slices approach infinity, we see that the area of the shaded region is |