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9. ↑ w In w dw 11. f (x² + 2x) cos x dx 13. fcos ¹x dx 15. ft²ln t di In 17. St csc²t dt 19. (In x)² dx 21. fe³ cos x dx 23. fe²⁰ sin 30 de In x 10. f flux d dx x² 12. ft² sin ßt dt 14. f In √x dx 16. f tan-¹(2y) dy 18. fxc 20. S 10- 22. fe* sin πx dx 24. Secos 20 de. x cosh ax dx dz

9. ↑ w In w dw 11. f (x² + 2x) cos x dx 13. fcos ¹x dx 15. ft²ln t di In 17. St csc²t dt 19. (In x)² dx 21. fe³ cos x dx 23. fe²⁰ sin 30 de In x 10. f flux d dx x² 12. ft² sin ßt dt 14. f In √x dx 16. f tan-¹(2y) dy 18. fxc 20. S 10- 22. fe* sin πx dx 24. Secos 20 de. x cosh ax dx dz

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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### Integral Calculus Practice Problems Here are some integral calculus problems for advanced students to practice. Try solving them on your own and verify your results with your peers or instructor. 1. \(\int w \ln w \, dw\) 2. \(\int \frac{\ln x}{x^2} \, dx\) 3. \(\int (x^2 + 2x) \cos x \, dx\) 4. \(\int t^2 \sin \beta t \, dt\) 5. \(\int \cos^{-1} x \, dx\) 6. \(\int \ln \sqrt{x} \, dx\) 7. \(\int t^4 \ln t \, dt\) 8. \(\int \tan^{-1} (2y) \, dy\) 9. \(\int t \csc^2 t \, dt\) 10. \(\int x \cosh(ax) \, dx\) 11. \(\int (\ln x)^2 \, dx\) 12. \(\int \frac{z}{10z} \, dz\) 13. \(\int e^{3x} \cos x \, dx\) 14. \(\int e^x \sin(\pi x) \, dx\) 15. \(\int e^{2 \theta} \sin(3 \theta) \, d\theta\) 16. \(\int e^{- \theta} \cos(2 \theta) \, d\theta\) ### Solutions and Tips: 1. This problem involves the integrand \(w \ln w\). Integration by parts might help. 2. This is an example of integrating functions involving natural logarithms. Consider substitution methods. 3. For this integral, the product of polynomials and trigonometric functions is tackled. Integration by parts is suitable. 4. Trigonometric integrals often use simple substitution or integration by parts. 5. Handling inverse trigonometric functions can be tricky; look at leveraging integration by parts. 6. The square root and logarithms combination may need substitution. 7. For integrals involving polynomials and logarithms, integration by parts is effective. 8. Inverse tangent functions might require specific techniques like trigonometric identities or substitution. 9. This involves csc squared; recall the standard integrals of trigonometric functions.
Transcribed Image Text:### Integral Calculus Practice Problems Here are some integral calculus problems for advanced students to practice. Try solving them on your own and verify your results with your peers or instructor. 1. \(\int w \ln w \, dw\) 2. \(\int \frac{\ln x}{x^2} \, dx\) 3. \(\int (x^2 + 2x) \cos x \, dx\) 4. \(\int t^2 \sin \beta t \, dt\) 5. \(\int \cos^{-1} x \, dx\) 6. \(\int \ln \sqrt{x} \, dx\) 7. \(\int t^4 \ln t \, dt\) 8. \(\int \tan^{-1} (2y) \, dy\) 9. \(\int t \csc^2 t \, dt\) 10. \(\int x \cosh(ax) \, dx\) 11. \(\int (\ln x)^2 \, dx\) 12. \(\int \frac{z}{10z} \, dz\) 13. \(\int e^{3x} \cos x \, dx\) 14. \(\int e^x \sin(\pi x) \, dx\) 15. \(\int e^{2 \theta} \sin(3 \theta) \, d\theta\) 16. \(\int e^{- \theta} \cos(2 \theta) \, d\theta\) ### Solutions and Tips: 1. This problem involves the integrand \(w \ln w\). Integration by parts might help. 2. This is an example of integrating functions involving natural logarithms. Consider substitution methods. 3. For this integral, the product of polynomials and trigonometric functions is tackled. Integration by parts is suitable. 4. Trigonometric integrals often use simple substitution or integration by parts. 5. Handling inverse trigonometric functions can be tricky; look at leveraging integration by parts. 6. The square root and logarithms combination may need substitution. 7. For integrals involving polynomials and logarithms, integration by parts is effective. 8. Inverse tangent functions might require specific techniques like trigonometric identities or substitution. 9. This involves csc squared; recall the standard integrals of trigonometric functions.
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