Consider the integral

where n is a positive integer.

(a) Is the integral improper? Explain.(b) Use a graphing utility to graph the integrand for n = 2, 4, 8, and 12.(c) Use the graphs to approximate the integral as n ∞.(d) Use a computer algebra system to evaluate the integral for the values of n in part (b). Make a conjecture about the value of the integral for any positive integer n. Compare your results with your answer in part (c).

Transcribed Image Text:

*π/2 4 1 + (tan x) dx