(Please extend sufficient space if you work on the docx version) 1. Use the definition of an improper integral to evaluate the following integrals. 1 (a) Jo 2-x dx (b) -$12 dx (c) dx 2. Determine whether the improper integral is convergent or divergent without solving the integral. Use an appropriate inequality to support your conclusion. 2x (a) - x3 + 3x2 + 2 dx J ( 9) 1 Vx - 1 dx 3. Complete the square in the denominator, make appropriate substitution, and integrate. 2x - 5 dx (Hint: 2x - 5 = 2x + 4-9) x2 + 4x +5 4. Evaluate the following integrals using the integration by parts. (a) (2x +3) cosxdx (b) [4x In xdx (c) [x'edx 5. Find the integral ( ex sin(x)dx (Hint: Reappearing Integral)