INSTRUCTIONS: solve the following and write the nal answer on the box provided; show complete solutions; provide drawings; etc.; hand written; refer to solution guidelines for other details. NOT FOLLOWING THE INSTRUCTIONS WILL BE GIVEN FULL DEDUCTIONS. PART I. INTEGRATION TECHNIQUE Integration by parts 1. [-5x2e-* dx 2. f 8 In x dx Algebraic Substitution x' dx 3. J 2vx2-9 4. -5 x1/2 (x + 1)-1/2dx Trigonometric Substitution 5. J f2 - x2 dx where f is constant 6. S Vx2-25 dx Rational Fractions 7. S (3-4X-1 x(x-1)3 11 x -8 8. dx (x-2) (x+2) PART II. APPLICATION 9. Find the area between the parabola x = 4 - y and the line y = 3 - x 10. Find the area between the x - axis and y = -2 + x2 11. Find the volume of the solid obtained by revolving the region bounded by the curves x2 = y, y = 0 and x = 2 about x - axis. 12. Find the volume of the solid obtained by revolving the region bounded by the curves y = 4 - x , y = 0 and x = 0 about y - axis