PLEASE SHOW WORK AND begin with a graph of the region FOR EACH QUESTION!

Find the areas of the regions enclosed by the lines and curves in #51-58.

\f75. The region bounded below by the parabola y = x2 and above by the line y = 4 is to be partitioned into two subsections of equal area by cutting across it with the horizontal line y = c. 3. Sketch the region and draw a line 32 = 6 across it that looks about right. In terms of 0, what are the coordinates of the points where the line and parabola intersect? Add them to your gure. b. Find 0 by integrating with respect to y. (This puts c in the limits of integration.) 6. Find c by integrating with respect to x. (This puts 6 into the integrand as well.) 79. The gure here shows triangle AOC inscribed in the region cut from the parabola y = x2 by the line y = a2. Find the limit of the ratio of the area of the triangle to the area of the parabolic region as a approaches zero. 87. If f is a continuous function, find the value of the integral a f(x) dx = f(x) + f(a - x) by making the substitution u = a - x and adding the resulting integral to