Explanation Given: The curves, y = 3 x and y = x 2 − 4 from x = − 1 to x = 3 . Formula used: Integration formula: ∫ x n d x = x n + 1 n + 1 + C Calculation: Area bounded by the two curves will be given by, ∫ − 1 3 [ 3 x − ( x 2 − 4 ) ] d x = 3 x 2 2 | − 1 3 − x 3 3

Mathematics with Applications, Books a la Carte, and MyLab Math with Pearson eText - Title-Specific Access Card Package (12th Edition)

12th Edition

ISBN: 9780134862651

Author: Lial

Publisher: PEARSON

See similar textbooks

Concept explainers

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 se…

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, integratio…

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 th…

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.

Videos

Question

Chapter 13.6, Problem 13E

To determine

To calculate: The area between the two curves y=3x and y=x2−4 from x=−1 to x=3.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 13.6, Problem 12E

Chapter 13.6, Problem 14E

Students have asked these similar questions

2. (i) Which of the following statements are true? Construct coun- terexamples for those that are false. (a) sequence. Every bounded sequence (x(n)) nEN C RN has a convergent sub- (b) (c) (d) Every sequence (x(n)) nEN C RN has a convergent subsequence. Every convergent sequence (x(n)) nEN C RN is bounded. Every bounded sequence (x(n)) EN CRN converges. nЄN (e) If a sequence (xn)nEN C RN has a convergent subsequence, then (xn)nEN is convergent. [10 Marks] (ii) Give an example of a sequence (x(n))nEN CR2 which is located on the parabola x2 = x², contains infinitely many different points and converges to the limit x = (2,4). [5 Marks]

2. (i) What does it mean to say that a sequence (x(n)) nEN CR2 converges to the limit x E R²? [1 Mark] (ii) Prove that if a set ECR2 is closed then every convergent sequence (x(n))nen in E has its limit in E, that is (x(n)) CE and x() x x = E. [5 Marks] (iii) which is located on the parabola x2 = = x x4, contains a subsequence that Give an example of an unbounded sequence (r(n)) nEN CR2 (2, 16) and such that x(i) converges to the limit x = (2, 16) and such that x(i) # x() for any i j. [4 Marks

1. (i) which are not. Identify which of the following subsets of R2 are open and (a) A = (1, 3) x (1,2) (b) B = (1,3) x {1,2} (c) C = AUB (ii) Provide a sketch and a brief explanation to each of your answers. [6 Marks] Give an example of a bounded set in R2 which is not open. (iii) [2 Marks] Give an example of an open set in R2 which is not bounded. [2 Marks]

Chapter 13 Solutions

Mathematics with Applications, Books a la Carte, and MyLab Math with Pearson eText - Title-Specific Access Card Package (12th Edition)

Ch. 13.1 - Checkpoint 1 Find an antiderivative for each of...Ch. 13.1 - Checkpoint 2 Find each of the...Ch. 13.1 - Prob. 3CP Ch. 13.1 - Prob. 4CP Ch. 13.1 - Prob. 5CP Ch. 13.1 - Prob. 6CP Ch. 13.1 - Prob. 7CP Ch. 13.1 - Checkpoint 8 The marginal cost at a level of...Ch. 13.1 - 1. What must be true of F(x) and G(x) if both are...Ch. 13.1 - 2. How is the antiderivative of a function related...

Knowledge Booster

Learn more about

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

The area between the two curves y = 3 x and y = x 2 − 4 from x = − 1 to x = 3 .

Concept explainers

Videos

To calculate: The area between the two curves y=3x and y=x2−4 from x=−1 to x=3.

Want to see the full answer?

Chapter 13 Solutions