# Worksheet: Reduction Formulae for Integration

In this worksheet, we will practice deriving reduction formulae and using them to evaluate integrals.

**Q1: **

Reduction formulas relate integrals involving an integer parameter. Let for .

What is ?

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Use , and integration by parts to derive a relation between and . Clear denominators if necessary.

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From your previous answer, find a formula for in terms of .

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Evaluate the indefinite integral .

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**Q2: **

The following table lists the integrals for , and 2.

0 | 1 | 2 | |

Use the table to predict a formula for and then verify this by differentiating.

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Write the and with which you can prove the formula using integration by parts.

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**Q3: **

Evaluate the indefinite integral .

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**Q4: **

Evaluate the indefinite integral .

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**Q5: **

Evaluate the indefinite integral .

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