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Determine which integration strategy will work the best for each integral. a. Partial Fraction Decomposition zp(z); b. Trigonometric Substitution c. Use Trigonometric Identities and then Substitution d. Split into two integrals -- Use Substition and Inverse Trig Function )sin³( 4т — 2 -dr e. Long Division then Partial Fraction Decomposition 1² – 10z + 34 2 -dr x² - 10z f. Substitution g. Integration By Parts dr 2x + 1 1² – 10z 1² · /4

Determine which integration strategy will work the best for each integral. a. Partial Fraction Decomposition zp(z); b. Trigonometric Substitution c. Use Trigonometric Identities and then Substitution d. Split into two integrals -- Use Substition and Inverse Trig Function )sin³( 4т — 2 -dr e. Long Division then Partial Fraction Decomposition 1² – 10z + 34 2 -dr x² - 10z f. Substitution g. Integration By Parts dr 2x + 1 1² – 10z 1² · /4

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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### Integration Techniques: Select the Best Strategy For each integral provided below, determine the most suitable integration strategy from the list on the right. Use the dropdown menus to match the integrals with the correct techniques. 1. \(\int x \sec(x) \tan(x) \, dx\) 2. \(\int \cos^3(x) \sin^5(x) \, dx\) 3. \(\int \frac{4x - 2}{x^2 - 10x + 34} \, dx\) 4. \(\int \frac{4x - 2}{x^2 - 10x} \, dx\) 5. \(\int \frac{x}{\sqrt{4 - x^2}} \, dx\) 6. \(\int \frac{x^3 - 2x + 1}{x^2 - 10x} \, dx\) 7. \(\int \frac{2}{x^2 \cdot \sqrt{4 - x^2}} \, dx\) #### Available Integration Strategies a. Partial Fraction Decomposition b. Trigonometric Substitution c. Use Trigonometric Identities and then Substitution d. Split into two integrals -- Use Substitution and Inverse Trig Function e. Long Division then Partial Fraction Decomposition f. Substitution g. Integration By Parts **Instructions:** Use the dropdown menus to select one of the seven strategies for each integral, ensuring the correct application of integration techniques. **Explanation of Techniques:** - *Partial Fraction Decomposition*: Useful for integrating rational functions where the degree of the numerator is less than the degree of the denominator. - *Trigonometric Substitution*: Applies to integrals involving expressions like \(\sqrt{a^2 \pm x^2}\), \(\sqrt{x^2 - a^2}\), etc. - *Using Trigonometric Identities and then Substitution*: Helpful in cases involving products of sine and cosine functions with different powers. - *Split into two integrals*: Approach by breaking complex integral into simpler parts and using substitution or other appropriate methods. - *Long Division then Partial Fraction Decomposition*: Applied when the degree of the numerator is greater than or equal to the degree of the denominator. - *Substitution*: Direct substitution to simplify the integral. - *Integration By Parts*: Typical for
Transcribed Image Text:### Integration Techniques: Select the Best Strategy For each integral provided below, determine the most suitable integration strategy from the list on the right. Use the dropdown menus to match the integrals with the correct techniques. 1. \(\int x \sec(x) \tan(x) \, dx\) 2. \(\int \cos^3(x) \sin^5(x) \, dx\) 3. \(\int \frac{4x - 2}{x^2 - 10x + 34} \, dx\) 4. \(\int \frac{4x - 2}{x^2 - 10x} \, dx\) 5. \(\int \frac{x}{\sqrt{4 - x^2}} \, dx\) 6. \(\int \frac{x^3 - 2x + 1}{x^2 - 10x} \, dx\) 7. \(\int \frac{2}{x^2 \cdot \sqrt{4 - x^2}} \, dx\) #### Available Integration Strategies a. Partial Fraction Decomposition b. Trigonometric Substitution c. Use Trigonometric Identities and then Substitution d. Split into two integrals -- Use Substitution and Inverse Trig Function e. Long Division then Partial Fraction Decomposition f. Substitution g. Integration By Parts **Instructions:** Use the dropdown menus to select one of the seven strategies for each integral, ensuring the correct application of integration techniques. **Explanation of Techniques:** - *Partial Fraction Decomposition*: Useful for integrating rational functions where the degree of the numerator is less than the degree of the denominator. - *Trigonometric Substitution*: Applies to integrals involving expressions like \(\sqrt{a^2 \pm x^2}\), \(\sqrt{x^2 - a^2}\), etc. - *Using Trigonometric Identities and then Substitution*: Helpful in cases involving products of sine and cosine functions with different powers. - *Split into two integrals*: Approach by breaking complex integral into simpler parts and using substitution or other appropriate methods. - *Long Division then Partial Fraction Decomposition*: Applied when the degree of the numerator is greater than or equal to the degree of the denominator. - *Substitution*: Direct substitution to simplify the integral. - *Integration By Parts*: Typical for
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