1. Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region. y = 6 + \sqrt{x}, y = 6 + (1/4) x
2. Sketch the region enclosed by x = 5 y^2 and x + y = 4. Decide whether to integrate with respect to x or y. Then find the area of the region.
3. Sketch the region enclosed by x + y^2 = 42 and x = y. Decide whether to integrate with respect to x or y. Then find the area of the region.
4. Find the area of the region enclosed between y = 3 sin(x) and y = 4 cos(x) from x=0 to x=0.7*pi. Hint: Notice that this region consists of two parts.
5. Find c > 0 such that the area of the region enclosed by the parabolas y = x^2 - c^2 and y = c^2 -x^2 is 30. c= 6. Find the area of the region bounded by the parabola y = 4 x^2, the tangent line to this parabola at (3, 36) and the x axis.