(a) Explanation Given information: The region bounded by the x axis, the curve y = 3 x 4 and the lines x = 1 and x = − 1 . Volume by Disks for Rotation About the x axis. V = ∫ a b A ( x ) d x = ∫ a b π [ R ( x ) 2 ] d x Calculation: Sketch the region bounded by the x axis, the curve y = 3 x 4 and the lines x = 1 and x = − 1 as shown in Figure 1. Refer to Figure 1. The radius of the disk R ( x ) = 3 x 4 . The limit of integration are a = − 1 and b = 1 . Find the volume of the solid for rotation about the x axis using disk method as shown below: V = ∫ a b π [ R ( x ) 2 ] d x Substitute 3 x 4 for R ( x ) , − 1 for a , and 1 for b (b) To determine Calculate the volume of the solid about the y axis. (c) To determine Calculate the volume of the solid about the line x = 1 . (d) To determine Calculate the volume of the solid about the line y = 3

University Calculus: Early Transcendentals (4th Edition)

4th Edition

ISBN: 9780134995540

Author: Joel R. Hass, Christopher E. Heil, Przemyslaw Bogacki, Maurice D. Weir, George B. Thomas Jr.

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 6, Problem 7PE

(a)

To determine

Calculate the volume of the solid about the x axis.

(b)

To determine

Calculate the volume of the solid about the y axis.

(c)

To determine

Calculate the volume of the solid about the line x=1.

(d)

To determine

Calculate the volume of the solid about the line y=3

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6, Problem 6PE

Chapter 6, Problem 8PE

Students have asked these similar questions

A body of mass m at the top of a 100 m high tower is thrown vertically upward with an initial velocity of 10 m/s. Assume that the air resistance FD acting on the body is proportional to the velocity V, so that FD=kV. Taking g = 9.75 m/s2 and k/m = 5 s, determine: a) what height the body will reach at the top of the tower, b) how long it will take the body to touch the ground, and c) the velocity of the body when it touches the ground.

A chemical reaction involving the interaction of two substances A and B to form a new compound X is called a second order reaction. In such cases it is observed that the rate of reaction (or the rate at which the new compound is formed) is proportional to the product of the remaining amounts of the two original substances. If a molecule of A and a molecule of B combine to form a molecule of X (i.e., the reaction equation is A + B ⮕ X), then the differential equation describing this specific reaction can be expressed as: dx/dt = k(a-x)(b-x) where k is a positive constant, a and b are the initial concentrations of the reactants A and B, respectively, and x(t) is the concentration of the new compound at any time t. Assuming that no amount of compound X is present at the start, obtain a relationship for x(t). What happens when t ⮕∞?

Consider a body of mass m dropped from rest at t = 0. The body falls under the influence of gravity, and the air resistance FD opposing the motion is assumed to be proportional to the square of the velocity, so that FD = kV2. Call x the vertical distance and take the positive direction of the x-axis downward, with origin at the initial position of the body. Obtain relationships for the velocity and position of the body as a function of time t.

Chapter 6 Solutions

University Calculus: Early Transcendentals (4th Edition)

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.