25. f z³e² dz 27. f (1 + x²) e ³ dx 29. f'x 3* dx 31. Ủy sinh y dy rs In R 33. 35. x 37. 39. Indr R² dR 41. x sin x cos x dx SS MM eM dM sin x ln(cos x) dx | cos x sinh x dx 26. 22 28. 30. S (arcsin x)² dx 1/2 xex (1 + x)² 32.²² In w dw 40. 0 sin 370 de 34.1² sin 21 dt 36. | arctan(1/x) dx 38. ² (In.x)² x3 dx dx dr √4+r² 42. fe sin(t - s) ds
25. f z³e² dz 27. f (1 + x²) e ³ dx 29. f'x 3* dx 31. Ủy sinh y dy rs In R 33. 35. x 37. 39. Indr R² dR 41. x sin x cos x dx SS MM eM dM sin x ln(cos x) dx | cos x sinh x dx 26. 22 28. 30. S (arcsin x)² dx 1/2 xex (1 + x)² 32.²² In w dw 40. 0 sin 370 de 34.1² sin 21 dt 36. | arctan(1/x) dx 38. ² (In.x)² x3 dx dx dr √4+r² 42. fe sin(t - s) ds
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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Question
37
Transcribed Image Text:Below are several integral expressions intended to help you practice and enhance your understanding of calculus. Each integral is selected to cover a broad range of techniques and concepts in integration.
1. \(\int z^3 e^{z^2} \, dz\)
2. \(\int (\arcsin x)^2 \, dx\)
3. \(\int (1 + x^2)e^{3x} \, dx\)
4. \(\int_0^{1/2} \theta \sin 3\pi \theta \, d\theta\)
5. \(\int_0^1 x 3^x \, dx\)
6. \(\int_0^1 \frac{xe^x}{(1 + x)^2} \, dx\)
7. \(\int_0^2 y \sinh y \, dy\)
8. \(\int_1^2 w^2 \ln w \, dw\)
9. \(\int_1^5 \frac{\ln R}{R^2} \, dR\)
10. \(\int_0^\pi x \sin x \cos x \, dx\)
11. \(\int_0^{2\pi} t^2 \sin 2t \, dt\)
12. \(\int_1^3 \arctan(1/x) \, dx\)
13. \(\int_1^5 \frac{M}{e^M} \, dM\)
14. \(\int_1^2 \frac{(\ln x)^2}{x^3} \, dx\)
15. \(\int_0^{\pi/3} \sin x \ln (\cos x) \, dx\)
16. \(\int_0^1 \frac{r^3}{\sqrt{4 + r^2}} \, dr\)
17. \(\int_0^\pi \cos x \sinh x \, dx\)
18. \(\int_0^1 e^{s} \sin(t - s) \, ds\)
Use these integrals to test your skills and apply various integration techniques you have learned. Try to identify the appropriate methods, such as substitution, integration by parts, partial fractions, or special functions, to evaluate these integrals.
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