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dx 7. (3 – 5x)*

dx 7. (3 – 5x)*

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Help me find dx for #7. I set my u = (3-5x)^-4

15-22. Subtle substitutions Evaluate the following integrals. Integrate using Table 8.1. ,and the but 502 9-32. Divisi EXAMPLE 6 Multiply by 1 Evalua itegrals. 1 – cos xr x + 9. %3D 1- cos x 1. t + Multiply by 1. 1- cos x dx 3-36. Со 1 Look back at Example 2 for another instance where multiplication of the integrand by I leads to an easier integral. There, we multiplied the numerator and denominator by e in order to prepare for 3. dx Simplify. 1 + cos x 1 – cos x %3D 1 + cos x cos x dx | 5. - cos? x sin' x 1 - cos x = %3D | a change of variables. cos x dx 7-40. M sin x cos x dx Split up the fraction. 7. 1 sin² x sin? x 1 , cot x = csc x = COS 19. sin x csc x cot x dx sin /- csc2 x dx Furth The fo 11. E Related Exercisen = -cot x + csc x + C. e?Vx+1 dx SECTION 8.1 EXERCISES Review Questions What change of variables would you use for the integral S(4 - 7x)- dx? 14. et dx e* + 1 13. to 1. e2r Before integrating, how would you rewrite the integrand of S(x* + 2)? dx? /T-కటు et 16. dx 15. e -2e* 4e State a trigonometric identity that is useful in evaluating S sin?x dx. 3. 12 sin' x dx cos x In*(x²) 17. 18. - 2x + 4 -dx. - 4. Describe a first step in integrating x - 1 x(3x + 2) cos'x dx sin° x 10 19. 20. 5. Describe a first step in integrating o Vx' + x² +4 .3 dx. Vx² – 4x - 9 dx 21. dx x10 – 2x + 10x2 + 1 dx. 22. - 6. Describe a first step in integrating + 1 -3 3x3 23-28. Splitting fractions Evaluate the following integrals. Basic Skills 7-14. Substitution Review Evaluate the following integrals. x + 2 dx x2 + 4 23. 5/2 - x!2 24. dx 8. (9x - 2) dx x3/2 7. 4. (3 – 5x)* sin t + tan t - 25. dt cos?t 4 + e 37/8 26. (2--) TT dx 4 9. sin 2x 130 10. 3-4x dx 27. 2 3x - V1 - x² dx .2 3x + 1 In 2x dx 28. 11. dx 12. V4 - 4 x 2.
Transcribed Image Text:15-22. Subtle substitutions Evaluate the following integrals. Integrate using Table 8.1. ,and the but 502 9-32. Divisi EXAMPLE 6 Multiply by 1 Evalua itegrals. 1 – cos xr x + 9. %3D 1- cos x 1. t + Multiply by 1. 1- cos x dx 3-36. Со 1 Look back at Example 2 for another instance where multiplication of the integrand by I leads to an easier integral. There, we multiplied the numerator and denominator by e in order to prepare for 3. dx Simplify. 1 + cos x 1 – cos x %3D 1 + cos x cos x dx | 5. - cos? x sin' x 1 - cos x = %3D | a change of variables. cos x dx 7-40. M sin x cos x dx Split up the fraction. 7. 1 sin² x sin? x 1 , cot x = csc x = COS 19. sin x csc x cot x dx sin /- csc2 x dx Furth The fo 11. E Related Exercisen = -cot x + csc x + C. e?Vx+1 dx SECTION 8.1 EXERCISES Review Questions What change of variables would you use for the integral S(4 - 7x)- dx? 14. et dx e* + 1 13. to 1. e2r Before integrating, how would you rewrite the integrand of S(x* + 2)? dx? /T-కటు et 16. dx 15. e -2e* 4e State a trigonometric identity that is useful in evaluating S sin?x dx. 3. 12 sin' x dx cos x In*(x²) 17. 18. - 2x + 4 -dx. - 4. Describe a first step in integrating x - 1 x(3x + 2) cos'x dx sin° x 10 19. 20. 5. Describe a first step in integrating o Vx' + x² +4 .3 dx. Vx² – 4x - 9 dx 21. dx x10 – 2x + 10x2 + 1 dx. 22. - 6. Describe a first step in integrating + 1 -3 3x3 23-28. Splitting fractions Evaluate the following integrals. Basic Skills 7-14. Substitution Review Evaluate the following integrals. x + 2 dx x2 + 4 23. 5/2 - x!2 24. dx 8. (9x - 2) dx x3/2 7. 4. (3 – 5x)* sin t + tan t - 25. dt cos?t 4 + e 37/8 26. (2--) TT dx 4 9. sin 2x 130 10. 3-4x dx 27. 2 3x - V1 - x² dx .2 3x + 1 In 2x dx 28. 11. dx 12. V4 - 4 x 2.
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