# Practice Problems

Site: | Saylor Academy |

Course: | MA005: Calculus I |

Book: | Practice Problems |

Printed by: | Guest user |

Date: | Saturday, July 13, 2024, 6:33 AM |

## Description

Work through the odd-numbered problems 1-69. Once you have completed the problem set, check your answers.

## Practice Problems

For problems 1 - 3, put and verify that

For problems 5 – 13 , use the suggested to find du and rewrite the integral in terms of and . Then find an antiderivative in terms of , and, finally, rewrite your answer in terms of .

For problems 15 – 25 , use the change of variable technique to find an antiderivative in terms of .

For problems 27 – 37 , evaluate the definite integrals.

43. Find the area under one arch of the graph.

Problems 45 – 53 , expand the integrand and then find an antiderivative.

Problems 53 – 63 , perform the division and then find an antiderivative.

The definite integrals in problems 65 – 69 involve areas associated with parts of circles (Fig. 2). Use your knowledge of circles and their areas to evaluate the integrals. (Suggestion: Sketch a graph of the integrand function.)

Source: Dale Hoffman, https://s3.amazonaws.com/saylordotorg-resources/wwwresources/site/wp-content/uploads/2012/12/MA005-5.7-Finding-Antiderivatives.pdf

This work is licensed under a Creative Commons Attribution 3.0 License.