Activity 6.5.2. In this activity we explore the improper integrals / } dx and 1 3,z dx. a. First we investigate / } dx. i. Use the First FTC to determine the exact values of fi } dx, flow } dx, and flowto 1 dx. Then, use your computational device to compute a decimal approximation of each result. ii. Use the First FTC to evaluate the definite integral fu dx (which results in an expression that depends on b). iii. Now, use your work from (ii.) to evaluate the limit given by lim L dx . b-+0o J1 X b. Next, we investigate , x3/ dx. i. Use the First FTC to determine the exact values of 1 32 dx, f 3, dx, and (100000 x3/2 dx. Then, use your calculator to compute a decimal approximation of each result. ii. Use the First FTC to evaluate the definite integral f 13/2 dx (which results in an expression that depends on b). iii. Now, use your work from (ii.) to evaluate the limit given by lim 6-+0o J X3/2 5dx. c. Plot the functions y = - and y = 3/2 on the same coordinate axes for the values x = 0.. . 10. How would you compare their behavior as x increases without bound? What is similar? What is different? d. How would you characterize the value of foodx? of 1 3/2 dx? What does this tell us about the respective areas bounded by these two curves for x 2 1