Numerical Integration Methods

1. [latex]0.696[/latex]
2. [latex]9.298[/latex]
3. [latex]0.5000[/latex]
4. [latex]{T}_{4}=18.75[/latex]
5. [latex]0.500[/latex]
6. [latex]1.2819[/latex]
7. [latex]0.6577[/latex]
8. [latex]0.0213[/latex]
9. [latex]1.5629[/latex]
10. [latex]1.9133[/latex]
11. [latex]\text{T(4)}=0.1088[/latex]
12. [latex]1.0[/latex]
13. Approximate error is [latex]0.000325[/latex].
14. [latex]0.1544[/latex]
15. [latex]6.2807[/latex]
16. [latex]4.606[/latex]
17. [latex]3.41[/latex] ft
18. [latex]{T}_{16}=100.125[/latex]; absolute error = [latex]0.125[/latex]
19. about [latex]89,250[/latex] m²
20. parabola

Error Analysis in Numerical Integration

1. [latex]\dfrac{1}{7938}[/latex]
2. [latex]\dfrac{81}{25,000}[/latex]
3. [latex]475[/latex]
4. [latex]174[/latex]

Improper Integrals

1. divergent
2. [latex]\dfrac{\pi }{2}[/latex]
3. [latex]\dfrac{2}{e}[/latex]
4. Converges
5. Converges to [latex]\dfrac{1}{2}[/latex]
6. [latex]−4[/latex]
7. [latex]\pi[/latex]
8. diverges
9. diverges
10. [latex]1.5[/latex]
11. diverges
12. diverges
13. diverges
14. Both integrals diverge.
15. diverges
16. diverges
17. [latex]\pi[/latex]
18. [latex]0.0[/latex]
19. [latex]0.0[/latex]
20. [latex]6.0[/latex]
21. [latex]\dfrac{\pi }{2}[/latex]
22. [latex]8\text{ln}\left(16\right)-4[/latex]
23. [latex]1.047[/latex]
24. [latex]-1+\dfrac{2}{\sqrt{3}}[/latex]
25. [latex]7.0[/latex]
26. [latex]\dfrac{5\pi }{2}[/latex]
27. [latex]3\pi[/latex]
28. [latex]\dfrac{1}{s},s>0[/latex]
29. [latex]\dfrac{s}{{s}^{2}+4},s>0[/latex]