8. If f is a continuous function with If f (m) dm : 8, show that there is a point c in the interval [1,3] with f(c) = 4. 3. Consider the region enclosed by the line 3; = a: 1 and the parabola y2 = 23: + 6. (a) Sketch the region and, noting that the region consists of two separate parts, set up an integral to nd the area. (To sketch the parabola, start With the sideways parabola a: : y2 and use graph transformations.) (b) Now rewrite the curves as functions of y and set up another integral to nd the area, this time looking at the curves on the right and left of the region, rather than on the top and bottom. (c) Evaluate both of your integrals and check that you get the same area