I if r >1 c if r = 1. 1 if r < 1 Let g(x) = (a) Compute the third right-endpoint approximation R3 for the area under g(x) between a = 0 and b = 3. Your answer will depend on c. What is R3 when c = 7? When c = 8? How much did your answer change when you changed c?
Optimization
Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.
Integration
Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.
Application of Integration
In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.
Volume
In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).
Area
Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.
![Problem #2
(x if x>1
Let g(r) = {c
if r = 1.
1 if x <1
(a) Compute the third right-endpoint approximation R3 for the area under g(x) between
a = 0 and b = 3. Your answer will depend on c. What is R3 when c = 7? When
c = 8? How much did your answer change when you changed c?
(b) Compute R. Your answer will not depend on c.
(c) Compute Re for the same area. Your answer will depend on c. What is Re when
c = 7? When c= 8? How much did your answer change?
C =
(d) Set up, but don't compute, and expression for Ry00 of the same area. What is the
difference between R300 when c= 7 and R300 when c = 8?
(e) Suppose c= 1. Now g(x) is continuous on [0, 3]. What is g(x) dæ?
(f) Even if c + 1, we still say o g(x) dx equals the value you computed in part (e).
That is, the value of g(x) at a single point doesn't matter when computing a definite
integral. Explain why this makes sense with Riemann approximations. [Hint: How
many terms of RN does c affect? What happens to these terms as N → 0?]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F89e4021b-b303-4721-9aec-e6bd00e0caf9%2Ff963465b-4051-46e6-bc6d-0f31b73294d9%2Fnbwz6nr_processed.png&w=3840&q=75)
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