(a) To determine Calculate the volume of the solid by revolving the region bounded by the curves along the line x = 1 using shell method. Explanation Given information: The equation of curves are y = x 4 and y = 4 − 3 x 2 . The equation of the line is x = 1 . Calculation: Provide the equation of curve as follows. y = x 4 (1) y = 4 − 3 x 2 (2) The limits are a = − 1 and b = 1 . The radius of the shell is ( 1 − x ) . Calculate the shell height as shown below. Shell height = 4 − 3 x 2 − x 4 Calculate the volume of the solid using shell method as shown below. V = ∫ a b 2 π ( shell radius ) ( shell height ) d x Substitute − 1 for a , 1 for b , 1 − x for shell radius, and 4 − 3 x 2 − x 4 for shell height. V = ∫ − 1 1 2 π ( 1 − x ) ( 4 − 3 x 2 − x 4 ) d x = 2 π ∫ − 1 1 ( 4 − 3 x 2 − x 4 − 4 x + 3 x 3 − x 5 ) d x = 2 π ( 4 x − 3 x 3 3 − (b) To determine Calculate the volume of the solid by revolving the region bounded by the curves along x axis using shell method.

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

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 6.2, Problem 26E

(a)

To determine

Calculate the volume of the solid by revolving the region bounded by the curves along the line x=1 using shell method.

(b)

To determine

Calculate the volume of the solid by revolving the region bounded by the curves along x axis using shell method.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6.2, Problem 25E

Chapter 6.2, Problem 27E

Students have asked these similar questions

Instructions. "I have written solutions in text form, but I need experts to rewrite them in handwriting from A to Z, exactly as I have written, without any changes."

Both in images okk. Instructions. "I have written solutions in text form, but I need experts to rewrite them in handwriting from A to Z, exactly as I have written, without any changes."

Question 1: If a barometer were built using oil (p = 0.92 g/cm³) instead of mercury (p = 13.6 g/cm³), would the column of oil be higher than, lower than, or the same as the column of mercury at 1.00 atm? If the level is different, by what factor? Explain. (5 pts) Solution: A barometer works based on the principle that the pressure exerted by the liquid column balances atmospheric pressure. The pressure is given by: P = pgh Since the atmospheric pressure remains constant (P = 1.00 atm), the height of the liquid column is inversely proportional to its density: Step 1: Given Data PHg hol=hgx Poil • Density of mercury: PHg = 13.6 g/cm³ Density of oil: Poil = 0.92 g/cm³ • Standard height of mercury at 1.00 atm: hμg Step 2: Compute Height of Oil = 760 mm = 0.760 m 13.6 hoil = 0.760 x 0.92 hoil = 0.760 × 14.78 hoil = 11.23 m Step 3: Compare Heights Since oil is less dense than mercury, the column of oil must be much taller than that of mercury. The factor by which it is taller is: Final…

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.