Explanation Given: The interval is [ 3 , 11 ] and n = 4 . Definition used: Suppose that f is defined and is integrable on [ a , b ] . The Midpoint Rule approximation to ∫ a b f ( x ) d x using n equally spaced subintervals on [ a , b ] is, M ( n ) = f ( m 1 ) Δ x + f ( m 2 ) Δ x + .... + f ( m n ) Δ x = ∑ k = 1 n f ( x k − 1 + x k 2 ) Δ x Where, Δ x = b − a n , x 0 = a , x k = a + k Δ x , and m k = x k − 1 + x k 2 is the midpoint of [ x k , x k − 1 ] , for k = 1 , 2 , 3... n . Calculation: The x coordinates of the integrant is m k ’s in Midpoint Rule approximation method (the Midpoint Rule approximation method is given above). If the interval [ a , b ] is partitioned into n equal intervals then, Δ x = b − a n

Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book

2nd Edition

ISBN: 9780321954237

Author: William L. Briggs, Lyle Cochran, Bernard Gillett

Publisher: PEARSON

See similar textbooks

Concept explainers

Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is…

Videos

Question

Chapter 7.7, Problem 1QC

To determine

To find: The points at which the integrand must be evaluated.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 7.6, Problem 82E

Chapter 7.7, Problem 2QC

Students have asked these similar questions

Question 1. (10 points) A researcher is studying tumours in mice. The growth rate for the volume of the tumour V(t) in cm³ is given by dV = 1.45V(2 In(V+1)). dt (a) (4 pts) Find all the equilibria and determine their stability using the stability condition. (b) (2 pts) Draw the phase plot f(V) versus V where f(V) = V'. You may find it helpful to use Desmos or Wolfram Alpha to plot the graph of f(V) versus V (both are free to use online), or you can plot it by hand if you like. On the plot identify each equilibrium as stable or unstable. (c) (4 pts) Draw direction arrows for the case where the tumour starts at size 3cm³ and for the case where the tumour starts at size 9cm³. Explain in biological terms what happens to the size of each of these tumours at time progresses.

For the system consisting of the two planes:plane 1: -x + y + z = 0plane 2: 3x + y + 3z = 0a) Are the planes parallel and/or coincident? Justify your answer. What does this tell you about the solution to the system?b) Solve the system (if possible). Show a complete solution. If there is a line of intersection express it in parametric form.

Question 2: (10 points) Evaluate the definite integral. Use the following form of the definition of the integral to evaluate the integral: Theorem: Iff is integrable on [a, b], then where Ax = (ba)/n and x₂ = a + i^x. You might need the following formulas. IM³ L² (3x² (3x²+2x- 2x - 1)dx. n [f(z)dz lim f(x)Az a n→∞ i=1 n(n + 1) 2 n i=1 n(n+1)(2n+1) 6

Chapter 7 Solutions

Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book

Ch. 7.1 - Prob. 1QC Ch. 7.1 - Prob. 2QC Ch. 7.1 - Prob. 3QC Ch. 7.1 - Prob. 4QC Ch. 7.1 - What change of variables would you use for the...Ch. 7.1 - Prob. 2E Ch. 7.1 - What trigonometric identity is useful in...Ch. 7.1 - Describe a first step in integrating x32x+4x1dx.Ch. 7.1 - Prob. 5E Ch. 7.1 - Prob. 6E

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.