Science:Math Exam Resources/Courses/MATH101/April 2008/Question 03 (c)/Solution 1

From UBC Wiki

We recognize a denominator of the form and so we attempt a trigonometric substitution of the form

Then the integral becomes

To solve this integral we use another substitution:

to obtain

To revert back to an expression with we have to calculate

Math Exam Resources Courses MATH101 April 2008 Question 3 (c) picture1.png

So we use a reference triangle. The sides and are given from the substitution With Pythagoras we can then calculate the length of the remaining side of the triangle, which is . Hence our final answer is