To determine To find: The volume of the solid of revolution formed when its rotating about the x axis where the region bounded by the curves f ( x ) = 1 − x 2 , y = 0 . Explanation Formula used: The volume of the solid formed by rotating R about the x axis is ∫ a b π f ( x ) 2 d x , where R is the region between f ( x ) and x -axis from x = a to x = b . Calculation: Calculate the volume of the solid when the region R is rotating about the- x axis. Here, f ( x ) = 1 − x 2 intersects y = 0 . Therefore, 1 − x 2 = y 1 − x 2 = 0 x 2 = 1 x = ± 1 Here, R is the region between f ( x ) = 1 − x 2 and x axis where x varies from − 1 to 1. Substitute the respective values in ∫ a b π f ( x ) 2 d x and evaluate. V = ∫ − 1 1 π ( 1 − x 2 ) 2 d x = ∫ − 1 1 π ( 1 2 + ( x 2 ) 2 − 2 <

Calculus With Applications, Books a la Carte Plus MyLab Math Package (11th Edition)

11th Edition

ISBN: 9780133886849

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

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 8.2, Problem 17E

To determine

To find: The volume of the solid of revolution formed when its rotating about the x axis where the region bounded by the curves f(x)=1−x2 , y=0 .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8.2, Problem 16E

Chapter 8.2, Problem 18E

Students have asked these similar questions

Q2/ verify that f grad = (h grad f- f grad h) h h₂ where and h are scalar factions. Solve in paper

This question is a previous exam question. I am using it for practice but am stuck

in Q. A firm price of 501: If the Total cast is given by perfect competition sells its products at the TTC = 3Q² +2Q+5. level of output will will be the level of profit at What What Devive the Consumer Curve approach. demand the function maximize this firm's, that using putput level. the indifference prpfit. Q₂. The Total Cost equation in the production of bacon has hypothetical factor a 2 A C= "TC 1000+ 159" +03 ; Where ç. Kash, Bacao - metric bone Compute and 11" tonnes the and average cost at output level of 10. Stretch theme marginal cost of the the shope Carve an the production average, Cost arve 12 tonnes and explain, the relationship between Marginal Cost product es tamen op d Galaxy A71 01 Curve in

Chapter 8 Solutions

Calculus With Applications, Books a la Carte Plus MyLab Math Package (11th Edition)

Ch. 8.1 - YOUR TURN 1 Find Ch. 8.1 - YOUR TURN 2 Find Ch. 8.1 - YOUR TURN 3 Find Ch. 8.1 - YOUR TURN 4 Find . Ch. 8.1 - YOUR TURN 5 Find Ch. 8.1 - Prob. 1WE Ch. 8.1 - Find the following. W2. Ch. 8.1 - Find the following. W3. Ch. 8.1 - Find the following. W4. Ch. 8.1 - Use integration by parts to find the integrals in...

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.