1. Integration by Substitution

2. Objectives Students will be able to Calculate an indefinite integral requiring the method of substitution.

3. Integration by Substitution Please note that g is continuous and differentiable and f(u) is continuous at all points u in the range of g.

4. Example 1 Evaluate the indefinite integral

5. Example 2 Evaluate the indefinite integral

6. Example 3 Evaluate the indefinite integral

7. Example 4 Evaluate the indefinite integral

8. Example 5 Evaluate the indefinite integral

9. Example 6 Evaluate the indefinite integral

10. Example 7 The marginal revenue (in thousands of dollars) from the sale of x gadgets is given by the function a.Find the total revenue function if the revenue from 115 gadgets is $45,581. b.How many gadgets must be sold for a revenue of at least $45,000?