Section 5.8

Substitution in Definite Integrals

When we change the variable, we must change the world. The bounds and are -values. They must be converted to -values.

1

Changing Worlds

This is cleaner than back-substituting because we never have to return to .

2

Worked Example

Polynomial Composite

Evaluate .

1. Substitution

2. Change Bounds (Critical!)

At
At

3. Evaluate New Integral

3

Level Up Examples

Example A: Trig Bounds

Evaluate .

1. Sub:

.

2. Bounds:

.

.

3. Result:

. (Flip bounds flips sign).

Example B: Logarithmic

Evaluate .

1. Sub:

.

2. Bounds:

.

.

3. Result:

.

5

Practice Quiz

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