sec7_3

# sec7_3 - 3 / 2) and use the identity tan 2 + 1 = sec 2...

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7.3 Trigonometric Substitution 1. Trig substitution rules Remark 1.1. This method should be used only after other methods such as standard substitution are ruled out. Integrals involving the form a 2 - x 2 : Substitute x = a sin θ ( - π/ 2 θ π/ 2) and use the identity sin 2 θ + cos 2 θ =1 Example 1.1. ± dx 16 - x 2 Integrals involving the form a 2 + x 2 : Substitute x = a tan θ ( - π/ 2 <θ< π/ 2) and use the identity tan 2 θ + 1 = sec 2 θ Example 1.2. ± 16 + 25 x 2 dx Integrals involving the form x 2 - a 2 : Substitute x = a sec θ (0 θ π/ 2 or π θ<

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Unformatted text preview: 3 / 2) and use the identity tan 2 + 1 = sec 2 Example 1.3. 6 2 dx x x 2-3 1 Section 7.3 Trigonometric Substitution 2 2. Mixed Examples Example 2.1. 2 1 dx 4-( x-1) 2 Example 2.2. 1 + x 2 x dx Example 2.3. dx x x 2 + 16 Section 7.3 Trigonometric Substitution 3 Example 2.4. x + 1 4-x 2 dx Example 2.5. dx x 2-2 x + 5 Example 2.6. 3 x 5-6 x + 9 x 2 dx...
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## sec7_3 - 3 / 2) and use the identity tan 2 + 1 = sec 2...

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