UIZ # 4 Problems (An answer, even if \"correct\" but lacking work, will NOT receive full credit!) 1. Use the definition of an improper integral to evaluate the following integrals. (a) 1 x 3 dx 4 (b) 4 1 0 5/ 2 1 x (c) x 1 5/2 dx dx 2. Determine whether the improper integral is convergent or divergent without solving the integral. Use an appropriate inequality to support your conclusion. (a) x 1 (b) 3 2x dx 3x 2 2 1 x 1 2 dx 3. Complete the square in the denominator, make appropriate substitution, and integrate. 1 x 2 2 x 10dx 4. Evaluate the following integrals using the integration by parts. (a) (3x 4) sin xdx (b) 2 x ln xdx (c) 2 x x e dx 5. Find the integral e 3x (Hint: Reappearing Integral) sin( x )dx