7 ## Approximating Integrals using Numerical Methods### Instructions:Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpson's Rule to approximate the given integral with the specified value of \( n \).### Given Integrals:7. \[\int_{0}^{1} \sqrt{1 + x^3} \, dx, \quad n = 4\]8. \[\int_{1}^{4} \sin \sqrt{x} \, dx, \quad n = 6\]9. \[\int_{0}^{1} e^x - 1 \, dx, \quad n = 10\]10. \[\int_{0}^{2} \sqrt[3]{1 - x^2} \, dx, \quad n = 10\]11. \[\int_{-1}^{2} e^{x + \cos x} \, dx, \quad n = 6\]12. \[\int_{1}^{3} e^{1/x} \, dx, \quad n = 8\]13. \[\int_{0}^{2} \sqrt{y} \cos y \, dy, \quad n = 8\]14. \[\int_{2}^{3} \frac{1}{\ln t} \, dt, \quad n = 10\]15. \[\int_{0}^{1} \frac{x^2}{1 + x^4} \, dx, \quad n = 10\]16. \[\int_{1}^{3} \frac{\sin t}{t} \, dt, \quad n = 4\]17. \[\int_{0}^{1} \ln(1 + e^x) \, dx, \quad n = 8\]18. \[\int_{0}^{1} \sqrt{1 + x^3} \, dx, \quad n = 10\]

Answered: Image /qna-images/answer/ea2dbdb5-12de-4df8-8244-80fac6ff394f.jpg

7-18 Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpson's Rule to approximate the given integral with the specified value of n. 7. ₁ √₁ + x³ dx, n = 4 9. ₁ √ex - 1 dx, n = 10 100 10. ²/1-x² dx, n = 10 2 11. ₁ ex+cosx dx, n = 6 -1 13. √y cos y dy, n = 8 x² 15. So 1 + x² 17. fln(1 + e*) dx, n = 8 C1 dx, n = 10 8. sin √x dx, n = 6 12. fe¹/x dx, 14. n = 8 12 d dt, n = 10 1 In t t 16. ₁ sin dt, n = 4

7-18 Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpson's Rule to approximate the given integral with the specified value of n. 7. ₁ √₁ + x³ dx, n = 4 9. ₁ √ex - 1 dx, n = 10 100 10. ²/1-x² dx, n = 10 2 11. ₁ ex+cosx dx, n = 6 -1 13. √y cos y dy, n = 8 x² 15. So 1 + x² 17. fln(1 + e*) dx, n = 8 C1 dx, n = 10 8. sin √x dx, n = 6 12. fe¹/x dx, 14. n = 8 12 d dt, n = 10 1 In t t 16. ₁ sin dt, n = 4

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: メ+1

Q: A = 6 -2 -2 10 -3 5 1 ---3-0 C=0-2 a = 1, b = [3 08]. -10 1 . B 5 2 11 9 4 4 7 0 0 11

A: We have to solve given Questions.

Q: 5.

Q: 40 -50-

Q: 8.20+2

Q: . 3류 - 2층 : 3% +4/3) 1

Q: 10 8/10 + 9 7/12=

Q: 5(18)

A: To find5(18)

Q: 2) 36³x=¹

Q: 1+3+5+7...+1003

A: Sum of n odd numbers, where the last term of the series is (2n – 1), is, Sn = 1 + 3 + 5 + …. + (2n –…

Q: 6.5+ 4

A: To simplify given

Q: Poove BLO => YQ< B.

Q: FIND S + 4 (s² – 8S + 6) -

Q: 4root2*4root2

Q: 7 2 3k+1= [A] k = 2

A: Consider the equation ∑n=273k+1=A We have to find the value of A Expand the summation of left hand…

Q: Expand (a −b)4

Q: 81 (1) 420

Q: 5 L s² + 2s – 3

A: We know that, Laplace transform of 1/(s-1) = e^t

Q: 10. Find the sum of the coefficients of (2x– 3)°. c. -6560 d. -5120 а. -5660 b. -6780

Q: 4. Fill in the following contingency table with the number of observations that fall into each com-…

A: x1 = number of colored oranges from Skittles brand = 77 x2 = number of colored oranges from M &…

Q: 7

Q: expansion of (1-2m)“

Q: 8 13

Q: 10| 5 10 10 -5 -5

Q: 18(9+7)+3

A: 18(9+7)+3

Q: 6. 3 (2s+5)³

Q: find: (m+I) m!

Q: 29 Using the combination formula expand (5+x)

Q: 6. Using the data from the contingency table, obtain the value of the test statistic of our test. 7.…

A: Step 1: Given: x1 = number of colored oranges from Skittles brand = 77 x2 = number of colored…

Q: 1. v₁ = (4, −2, 6, −4), V₂ = (6, −3, 9, −6)

Q: expand (x+y)6

Q: In a rectangle, the width is one-third the length. The total perimeter is 40 inches. Find the length…

A: Solution: Given: Width is one third of the length of rectangle and the perimeter of rectangle…

Q: 3(m – 5) + m

A: 3(m-5)+m=0 3m-15+m=0 add both side 15 we get 2m=15

Question

## Approximating Integrals using Numerical Methods

### Instructions:
Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpson's Rule to approximate the given integral with the specified value of \( n \).

### Given Integrals:

7. \[
\int_{0}^{1} \sqrt{1 + x^3} \, dx, \quad n = 4
\]

8. \[
\int_{1}^{4} \sin \sqrt{x} \, dx, \quad n = 6
\]

9. \[
\int_{0}^{1} e^x - 1 \, dx, \quad n = 10
\]

10. \[
\int_{0}^{2} \sqrt[3]{1 - x^2} \, dx, \quad n = 10
\]

11. \[
\int_{-1}^{2} e^{x + \cos x} \, dx, \quad n = 6
\]

12. \[
\int_{1}^{3} e^{1/x} \, dx, \quad n = 8
\]

13. \[
\int_{0}^{2} \sqrt{y} \cos y \, dy, \quad n = 8
\]

14. \[
\int_{2}^{3} \frac{1}{\ln t} \, dt, \quad n = 10
\]

15. \[
\int_{0}^{1} \frac{x^2}{1 + x^4} \, dx, \quad n = 10
\]

16. \[
\int_{1}^{3} \frac{\sin t}{t} \, dt, \quad n = 4
\]

17. \[
\int_{0}^{1} \ln(1 + e^x) \, dx, \quad n = 8
\]

18. \[
\int_{0}^{1} \sqrt{1 + x^3} \, dx, \quad n = 10
\]

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: Given data

VIEW

Step 2: Find the integral using Trapezoidal rule

VIEW

Step 3: Find the integral using Midpoint rule and Simpson's rule

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

6 1/6 + 6
5 -10-8 -6 14 -2 2 4 6 8 10 3 4 5 6 7 1
8(14-9)+5 32+6
Expand 2(c+ 3). 2(c + 3) = D
#5,6,7
7 3 -4 1 -1 0 0 0 1 -2 1 3 7. 1
37in 2o00
Find a basis for the space of 2 by 3 matrices whose nullspace contains (2, 1, 1 ).
19 a-c
11 12 X #I 4