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15.2 – The Substitution Rule

15.2 – The Substitution Rule. Example. 1. Evaluate . 2. Evaluate . 3. Evaluate . The Substitution Rule. u. du. Since, . Examples - Evaluate. The Substitution Rule – General Technique. Let u be g ( x ). You may wish to rearrange the function so that g’(x) is in front of the dx .

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15.2 – The Substitution Rule

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  1. 15.2 – The Substitution Rule

  2. Example 1. Evaluate 2. Evaluate 3. Evaluate

  3. The Substitution Rule u du Since,

  4. Examples - Evaluate

  5. The Substitution Rule – General Technique • Let u be g(x). You may wish to rearrange the function so that g’(x) is in front of the dx. • Determine du/dx and multiply both sides by dx. Verify that g’(x) also appears in the integrand. (It’s ok if it’s just off by a constant) • Make the substitution and everything must be written in terms of new variables u. (You need to modify the integrand first if the derivative in step 2 is off by a constant)

  6. Examples - Evaluate

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