Solutions to U-Substitution Practice Problems

Home > Review of First & Second Year Calculus > U-Substitution > PProb Solutions

Practice Problem Solutions: Problem 1 :: Problem 2 :: Problem 3

PROBLEM 1:

Problem: Evaluate using u-substitution.

Solution: Let . Then and . Thus we have the integral . Proceeding with normal integration, we find

PROBLEM 2:

Problem: Evaluate using u-substitution.

Solution: Let . Then we have and the integral . Integrating, we find .

PROBLEM 3:

Problem: Evaluate using u-substitution.

Solution: Most students will see the answer to this problem intuitively, but it can carefully found using u-substitution. Since , we have . Let , so and . Thus, we get . Integration gives us .
Note that the method used above made use of the exponent rule . One can use u-substitution to solve the problem as it is written without making use of this exponent rule. To do this, let . Then is also , so we have . The integral becomes , which is the same answer we obtained using the first method.

 

This page last updated 12 January, 2008 11:26 AM