# At a Glance - Thinking Backwards

"Thinking backwards" shows up in a lot of places. That means it must be important! Here, "thinking backwards" means instead of using a known integral value to evaluate an expression, we'll work backwards from an equation to find the integral value.

Think of the integral you're looking for as a unit. Instead of solving for *x*, you'll be solving for something like *. *If your equation contains a slightly different integral than the one you want, use the properties to manipulate the integral until it's what you're looking for.

#### Example 1

Find given that |

#### Example 2

Find given that |

#### Example 3

Combine the tricks used in the previous two examples to find given that |

#### Example 4

Find assuming that |

#### Exercise 1

Find given that

#### Exercise 2

Find given that

#### Exercise 3

Find given that

#### Exercise 4

Find given that *f* (*x*) is even and that

#### Exercise 5

Find given that *f* is odd and

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