Explanation Given: The integral is ∫ 2 10 x x − 1 d x and n = 4 Approach: Simpson’s rule- Let f be a continuous function on interval [ a , b ] . We subdivide the interval into n number of pieces. Length of each subinterval is Δ x = b − a n End points of each subinterval is x 0 = a x 1 = a + Δ x x 2 = a + 2 Δ x x 3 = a + 3 Δ x . . . x n = a + n Δ x Hence approximation of integral according to Simpson’s rule is ∫ a b f ( x ) d x = Δ x 3 [ f ( x 0 ) + 4 f ( x 1 ) + 2 f ( x 2 ) + 4 f ( x 3 ) + 2 f ( x 4 ) + ........... + 4 f ( x n − 1 ) + f ( x n ) ] Calculation: Given integral is ∫ 2 10 x x − 1 d x We have a = 2 , b = 10 Therefore length of each subinterval is Δ x = 10 − 2 4 = 8 4 = 2 End point of each subinterval is x 0 = 2 x 1 = 2 + 2 = 4 x 2 = 2 + 2 × 2 = 6 x 3 = 2 + 3 × 2 = 8 x 4 = 2 + 4 × 2 = 10 We have to find value of function at each end point of interval. Hence value of function at x = 2 f ( 2 ) = 2 2 − 1 = 2 Value of function at x = 4 f ( 4 ) = 4 4 − 1 = 4 3 = 1.3333 Value of function at x = 6 f ( 6 ) = 6 6 − 1 = 6 5 = 1

Pearson eText for Calculus for the Life Sciences -- Instant Access (Pearson+)

2nd Edition

ISBN: 9780137553457

Author: Raymond Greenwell, Nathan Ritchey

Publisher: PEARSON+

See similar textbooks

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

Videos

Question

Chapter 8.CR, Problem 20CR

To determine

To find:

Approximate the integral ∫210xx−1dx using Simpson’s rule with n=4 and also compare it with exact value of integral.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8.CR, Problem 19CR

Chapter 8.CR, Problem 21CR

Students have asked these similar questions

Find the differential of the function f(x, y) = −8x√y at the point (1,3) using Ax = 0.25 and Ay = -0.15. dz Now find Az and compare it to your answer above Az = Hint: If entering a decimal, round to at least 5 places

please dont use chat gpt i need to under

Chris Lynch plans to invest $200 into a money market account. Find the interest rate that is needed for the money to grow to $1,800 in 12 years if the interest is compounded quarterly. The rate is %. (Round to the nearest percent.)

Chapter 8 Solutions

Pearson eText for Calculus for the Life Sciences -- Instant Access (Pearson+)

Ch. 8.1 - YOUR TURN Use the trapezoidal rule with n=4 to...Ch. 8.1 - Prob. 2YT Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E Ch. 8.1 - Prob. 8E

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Approximate the integral ∫ 2 10 x x − 1 d x using Simpson’s rule with n = 4 and also compare it with exact value of integral.

Solution Summary: The author explains how to approximate the integral using Simpson's rule with n=4 and compare it with exact value of integral.

Concept explainers

Videos

To find:

Approximate the integral ∫210xx−1dx using Simpson’s rule with n=4 and also compare it with exact value of integral.

Want to see the full answer?

Chapter 8 Solutions

Approximate the integral ∫ 2 10 x x − 1 d x using Simpson’s rule with n = 4 and also compare it with exact value of integral.

Solution Summary: The author explains how to approximate the integral using Simpson's rule with n=4 and compare it with exact value of integral.

Concept explainers

Videos

To find: Approximate the integral ∫210xx−1dx using Simpson’s rule with n=4 and also compare it with exact value of integral.

Want to see the full answer?

Chapter 8 Solutions

To find:

Approximate the integral ∫210xx−1dx using Simpson’s rule with n=4 and also compare it with exact value of integral.