(a) Explanation Given information: Consider ℜ 1 is the region bounded by the curves y = x 2 , y = 0 and x = b . Consider ℜ 2 is the region bounded by the curves y = x 2 , x = 0 and y = b 2 . Calculation: Let ℜ 1 is the region below the graph of y = x 2 and above the x -axis between x = 0 and x = b . Let ℜ 2 is the region to the left of graph of x = y and to the right of the y axis between y = 0 and y = b 2 . Find the area region ℜ 1 bounded by the curves y = x 2 as shown below: A 1 = ∫ 0 b x 2 d x (1) Apply the integration in Equation (1): A 1 = [ 1 3 x 3 ] 0 b = b 3 3 Thus, the area of region ℜ 1 bounded by the curve is b 3 3 (b) To determine To find : the values of b such that ℜ 1 sweeps out the same volume when rotated about the x axis and y axis. (c) To determine To find : the values of b such that ℜ 1 sweeps out the same volume when rotated about the x axis. (d) To determine To find : the values of b such that ℜ 1 sweeps out the same volume when rotated about the y axis.

8th Edition

ISBN: 9781305756083

Author: James Stewart

Publisher: CENGAGE C

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, Problem 34RE

(a)

To determine

To find: the values of b such that the regions ℜ1 and ℜ1 have the same area.

(b)

To determine

To find: the values of b such that ℜ1 sweeps out the same volume when rotated about the x axis and y axis.

(c)

To determine

To find: the values of b such that ℜ1 sweeps out the same volume when rotated about the x axis.

(d)

To determine

To find: the values of b such that ℜ1 sweeps out the same volume when rotated about the y axis.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6, Problem 33RE

Chapter 6, Problem 1P

Students have asked these similar questions

A helicopter pilot needs to travel to a regional airport 25 miles away. She flies at an actual heading of N16.26°E with an airspeed of 110 mph, and there is a wind blowing directly east at 20 mph. (a) Determine the compass heading that the pilot needs to reach her destination. (b) How long will it take her to reach her destination?

Question 3. the given integral is convergent or divergent: Use the comparison test to determine whether or not * sin*(x + 1) 7x3 (a) |. d.x g8 + x4 + 1 -dx (b) 2.x4 + x + 1

-d.x tan x

Chapter 6 Solutions

ACP CALCULUS UCI: MATH 2A/2B

Ch. 6.1 - Find the area of the shaded region.Ch. 6.1 - Find the area of the shaded region.Ch. 6.1 - Find the area of the shaded region.Ch. 6.1 - Find the area of the shaded region.Ch. 6.1 - Sketch the region enclosed by the given curves....Ch. 6.1 - Sketch the region enclosed by the given curves....Ch. 6.1 - Sketch the region enclosed by the given curves....Ch. 6.1 - Sketch the region enclosed by the given curves....Ch. 6.1 - Sketch the region enclosed by the given curves....Ch. 6.1 - Sketch the region enclosed by the given curves....

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 values of b such that the regions ℜ 1 and ℜ 1 have the same area.

Solution Summary: The author explains that the values of b are underset_bne 0.

Concept explainers

Videos

To find: the values of b such that the regions ℜ1 and ℜ1 have the same area.

To find: the values of b such that ℜ1 sweeps out the same volume when rotated about the x axis and y axis.

To find: the values of b such that ℜ1 sweeps out the same volume when rotated about the x axis.

To find: the values of b such that ℜ1 sweeps out the same volume when rotated about the y axis.

Want to see the full answer?

Chapter 6 Solutions