Science:Math Exam Resources/Courses/MATH105/April 2016/Question 01 (l)/Solution 1
The region bounded by the function and x-axis from is
We first note that this is an improper integral, and we need to rewrite it as the following:
We now apply the substitution to simplify the integral. Note that and since is changing between and then is changing between and .
Therefore,
=
We know that the area of the region is 1. This implies that
We finally get