UIZ # 4 Problems 1. Use the definition of an improper integral to evaluate the following integrals. (a) 1 dx 2 x 2 0 (b) 5 1 0 5/ 2 x (c) 2 e 1 x dx dx 2. Determine whether the improper integral is convergent or divergent without solving the integral. (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. (Hint: ) 2x 5 2 x 5=2 x+ 49 x 2 4 x 5dx 4. Evaluate the following integrals using the integration by parts. (a) (2 x 3) cos xdx (b) 4 x ln xdx (c) 2 x x e dx 5. Find the integral e 3x (Hint: Reappearing Integral) sin( x)dx \f\f