Trigonometric Substitution

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Presentation transcript:

Trigonometric Substitution Lesson 9.6

New Patterns for the Integrand Now we will look for a different set of patterns And we will use them in the context of a right triangle Draw and label the other two triangles which show the relationships of a and x a x

Use identity tan2x + 1 = sec2x Example 3 x θ Given Consider the labeled triangle Let x = 3 tan θ (Why?) And dx = 3 sec2 θ dθ Then we have Use identity tan2x + 1 = sec2x

Finishing Up Our results are in terms of θ We must un-substitute back into x Use the triangle relationships 3 x θ

Knowing Which Substitution

Try It!! For each problem, identify which substitution and which triangle should be used

Keep Going! Now finish the integration

Application Find the arc length of the portion of the parabola y = 10x – x2 that is above the x-axis Recall the arc length formula

Assignment Lesson 9.6 Page 386 Exercises 1 – 33 (every other odd) Also 37, 39, and 41