1. Use the definition of an improper integral to evaluate: (a) 100 2 dx J1 ex (b) Jo V2-x = dx (c) J1 75/2 dx 2. Determine whether the improper integral is convergent or divergent without solving the integral: 2x (a) J1 x 3 + 3 x 2 + 2 -dx ( b) . - dx J2 Vx-1 3. Integrate: (a) Sex sin( ex) dx (b) S cos( x) sin* (x)dx 4. Complete the square in the denominator, make appropriate substitution, and integrate: (a) dx x2- 2x+10 2x-3 (b) x2 +4x+5 -dx (Hint:2x - 3 = 2x + 4 - 7) 5. Evaluate the following integrals using the integration by parts: (a) S x2ex dx SVx . In(x) dx (c) J e3x sin(x) dx