Explanation 1) Concept: The area A of the region bounded by the curves x = f y & x = g y , and the lines y = c , y = d , where f and g are continuous and f y ≥ g ( y ) for c ≤ y ≤ d , then area is A = ∫ c d f y - g y d y 2) Given: The region bounded by the curves x + y = 0 and x = y 2 + 3 y 3) Calculation: As the given region is bounded by the curves x + y = 0 and x = y 2 + 3 y , From the graph, the right boundary curve is x + y = 0 ⇒ x = - y and the left boundary curve is x = y 2 + 3 y x = - y and x = y 2 + 3 y intersect each other when, - y = y 2 + 3 y y 2 + 4 y = 0 , y y + 4 = 0 y = 0 o r y = - 4 Therefore, the area of the region bounded by the curves x = - y and x = y 2 + 3 y between x = - 4 to x = 0 is given by A =

8th Edition

ISBN: 9781285740621

Author: James Stewart

Publisher: Cengage Learning

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 5.R, Problem 4E

To determine

To find:

The area of region bounded by given curves.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 5.R, Problem 3E

Chapter 5.R, Problem 5E

Students have asked these similar questions

On from the equation: 2 u = C₁ + C₂ Y + Czy + Cu y³ Find C₁, C₂, C3 and Cy Using these following Cases : (a) 4=0 at y=0 (b) U = U∞ at y = 8 du (c) at Y = S ду --y. ди = 0 at y = 0 буг

Tips S ps L 50. lim x2 - 4 x-2x+2 51. lim 22 - X 52. 53. x 0 Answer lim x 0 lim 2-5 X 2x2 2 x² Answer -> 54. lim T - 3x - - 25 +5 b+1 b3b+3 55. lim X x-1 x 1 Answer 56. lim x+2 x 2 x 2 57. lim x²-x-6 x-2 x²+x-2 Answer-> 23-8 58. lim 2-22-2

S 36. lim 5x+2 x-2 37. lim √√2x4 + x² x-3 Answer-> 2x3 +4 38. lim x12 √ x² + 1 √√x² + 8 39. lim x-1 2x+4 Answer 40. lim x3 2x x√x² + 7 √√2x+3

Chapter 5 Solutions

Calculus (MindTap Course List)

Ch. 5.1 - Find the area of the shaded region.Ch. 5.1 - Find the area of the shaded region.Ch. 5.1 - Prob. 3E Ch. 5.1 - Find the area of the shaded region.Ch. 5.1 - Sketch the region enclosed by the given curves....Ch. 5.1 - Sketch the region enclosed by the given curves....Ch. 5.1 - Sketch the region enclosed by the given curves....Ch. 5.1 - Sketch the region enclosed by the given curves....Ch. 5.1 - Sketch the region enclosed by the given curves....Ch. 5.1 - Prob. 10E

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.

The area of region bounded by given curves.

Solution Summary: The author explains how the area of the region bounded by the curves x+y=0 and x=y2+3y is given.

Concept explainers

Videos

To find: The area of region bounded by given curves.

Want to see the full answer?

Chapter 5 Solutions

To find:

The area of region bounded by given curves.