Science:Math Exam Resources/Courses/MATH105/April 2018/Question 06/Solution 1

From UBC Wiki

By the fundamental theorem of calculus, for every , we have

Using linearity of the derivative and the chain rule, we then get
Since for , we can divide both sides of this equation by , which leaves . Now by the power rule for integration, we get that , for some constant .

To find the constant , observe that and

It follows that , or . Hence, we conclude that .

Answer: