typewritten with graph solution must be like of the reference example

Plane Areas by Integration Example 3. Find the area between the curves x2 = 2ay and x2 = 4ay - a . Solution. x =2ay x = 4ay - a- a * 2 x 0+2ata X 0 A=20 dx 4 0 4a 0 a 12 a 0 dA =()2 -V,)dx A= a dx a 0 =dava A =S (v2 -V1)dx 3 A= ax A=2/ (>2 - V1)dx 2 3a o 3 a 0 a x'+a x2 A= a 0 = Lay A=2 dx 2 3 a 4a 2 a 1 2 a2 A= X X 2 --3 A=2 a - + dxa = 4 2a 3 a sq. units 0 4 a. Solve the following applications of integral calculus. (5 points each) 1. Find the area of the region bounded by the xaxls, the line .1: = 2 and the graph of y = x3 1. 2. Find the area of the region on the l\" quadrant bound by the line .1: = 2 and the graph of y = [11: 1|. 3. Find the volume generated by revolving the rst-quadrant area bounded by the parabola y' = 31' and its latus rectum (x = 2) about the xaxls. 4. Find the volume generated when the plane area bounded by y = 2.1". y = 0. x = 0 and x = 5 is revolved about the y-axis