Name: answer key: (12 points) let r be the region bounded by y = 5 x2 and y = x + 3. (a) sketch the region r. [warning: one of the integrals below will have to be split into 2 pieces. ] The region is bounded by a parabola opening downward and a line (as pictured to the right). We need to know the points of intersection, so we set the bounds equal to each other: 5 x2 = x + 3. This means the graphs cross when x = 1 and x = 2. Notice that 5 ( 1)2 = 4 = ( 1) + 3 and. Thus the points of intersection are (x, y) = ( 1, 4) and (2, 1). First, as a y-simple region, the line is the bottom and the parabola is the top. So x + 3 y 5 x2. The points of intersect tell us that 1 x 2.
