1. Use the definition of an improper integral to evaluate: (a) - dx (b) 2 1 Jo V2-X = dx (c) x5/2 dx 2. Determine whether the improper integral is convergent or divergent without solving the integral: (a) 2x 1 7 3 +3 x 2 +2 -dx (b) 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 (b) 2x-3 dx x2+4x+5 (Hint:2x - 3 = 2x + 4- 7) 5. Evaluate the following integrals using the integration by parts: (a) Sx2exdx (b) SVx . In(x) dx (c) J e 3x sin(x)dx