Question: Let f(x) = c, where c > 0, be a constant function on [a, b]. Prove that any Riemann sum for any value of n

Let f(x) = c, where c > 0, be a constant function on [a, b]. Prove that any Riemann sum for any value of n gives the exact area of the region between the graph of f and the x-axis on [a, b].

Step by Step Solution

★★★★★

3.41 Rating (164 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Because the function f is constant its value is c at ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Calculus Early Transcendentals Questions!

Determine whether the following statements are true and give an explanation or counterexample. a. If f is a constant function on the interval [a, b], then the right and left Riemann sums give the...

Assume that the linear function f(x) = mx + c is positive on the interval [a, b]. Prove that the midpoint Riemann sum with any value of n gives the exact area of the region between the graph of f and...

Consider the function f(x) = 3x + 4 on the interval [3, 7]. Show that the midpoint Riemann sum with n = 4 gives the exact area of the region bounded by the graph.

Mohammed Yaaseen Gomdah E WeBWorK assignment due : 03/09/2016 at 03:00am EST. 1. (1 pt) Using disks or washers, nd the volume of the solid obtained by rotating the region bounded by the curves y =...

Height (meters) The figure above is the graph of a function of x, which models the height of a skateboard ramp. The function meets the following requirements. (i) At X = 0, the value of the function...

Hw1,2 1. For 0 l. For 0 S x 1, let f (x) = kx(l x), where k is a constant. (a) Find the value of k such that fis a density function. (b) What is the mean value of this random variable? (c) What is...

Let X denote a random variable supported on [0, 1] with pdf f (x) = c x2, where c is some constant. This question has to be answered analytically without using R. (a) Compute the value of c. (b)...

1. (60 pts True/False. Indicate whether the statement is true or false. If the statement is false, present an explanation or counterexample. (No explanation necessary for each true statement.) (2...

2.7. Explicit Solutions to Dierential Equations 109 power (kw) 20 15 10 5 0 08:00 10:00 12:00 14:00 16:00 time 18:00 2.7 Explicit Solutions to Dierential Equations In the very rare case in which an...

Planning Demand and Supply in a Supply Chain Capacity Planning and Assignment 1 utdallas.edu/~metin Outline Capacity Planning Product-to-plant Assignment utdallas.edu/~metin 2 Deterministic Capacity...

1. Who prevails and why? 2. Is this information necessary for Infinites case? Why or why not?

I need Thank you's inventory process. It is an Australian company called Thank you Companys inventory policy (raw materials inventory, work-in-process inventory, finished goods inventory) in...

C + + Task Description: You are keeping the scores for a baseball game with strange rules. At the beginning of the game, you start with an empty record. You are given a list of strings operations,...

What makes international corporate finance uniquely different from domestic corporate finance.

Find all values of x in the interval [0, 2] that satisfy the equation. 2 + cos 2x = 3 cos x

Find all values of x in the interval [0, 2] that satisfy the inequality. sin x 1/2

Find all values of x in the interval [0, 2] that satisfy the inequality. 2 cos x + 1 > 0

You plan to borrow $1,000,000 for buying a house. You have decided to go with bank XYZ which offers you an interest rate of 5% with daily compounding. 1.) Assume that you pay for the loan over 25...

For the regression model Y = B1 + B2X2 + B3X3 + e, the following estimation results are obtained: Regression Results coefficient estimate stanadard error B1 0.7 0.5 B2 4.9 8.3 B3 7.2 8.3 What is the...

1) (30 p.) Acme Molding is examining five alternatives for a piece of material handling equipment. Each has an expected life of 8 years with no salvage value, and Acme's MARR is 14%. Using an...