Use the definition of an improper integral to evaluate the given integral. Use a change of variable if necessary. Note: Integration calculator programs may have problems obtaining the correct answer for improper integrals because of the difficulties in evaluating the infinities. So use with caution. Better yet, solve analytically. 1. (10 pts) Jo V8-2x dx (similar to 8.1 #1-21) 2. (10 pts) Jo x 2 V27-x3 dx (similar to 8.1 #1-21) 3. (10 pts) "tan(x) dx (similar to 8.1 #1-21) Find the indefinite integrals and evaluate the definite integrals. In some problems a particular change of variable is suggested. 4. (10 pts) J 3x-3 x2 -2x+7 - dx, u = x2 - 2x + 7 (similar to 8.2 #1-42) 5. (10 pts) J sec ( 3-In(x) ) 'dx, u = 3 - In(x) (8.2 #18) x a. Use the integration table if necessary. (State which integral in the table you used.) http://scidiv.bellevuecollege.edu/dh/Calculus_all/CalculusRefFacts b. Now use one of the three integration programs list in the Summary Week 2 #12, #13, or #14. Submit a screenshot of your computer answer. c. Are your answers the same? (yes or no) 6. (10 pts) 4x+7 x2+2x+5 dx (8.2 #49-54)