BuyFind

Calculus (MindTap Course List)

8th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781285740621
BuyFind

Calculus (MindTap Course List)

8th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781285740621

Solutions

Chapter
Section
Chapter 8.R, Problem 2CC
Textbook Problem

(a) Write an expression for the surface area of the surface obtained by rotating the curve y = f ( x ) ,   a x b , about the x-axis.

(b) What if x is given as a function of y?

(c) What if the curve is rotated about the y-axis?

Expert Solution

Want to see this answer and more?

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

See solution

Chapter 8 Solutions

Calculus (MindTap Course List)
Show all chapter solutions
Ch. 8.1 - Find the exact length of the curve. y=x33+14x,1x2Ch. 8.1 - Find the exact length of the curve. x=y48+14y2,1y2Ch. 8.1 - Find the exact length of the curve. x=13y(y3),1y9Ch. 8.1 - Find the exact length of the curve....Ch. 8.1 - Find the exact length of the curve....Ch. 8.1 - Find the exact length of the curve....Ch. 8.1 - Find the exact length of the curve....Ch. 8.1 - Find the exact length of the curve. y=xx2+sin1(x)Ch. 8.1 - Find the exact length of the curve. y=ln(1x2),0x12Ch. 8.1 - Find the exact length of the curve. y=1ex,0x2Ch. 8.1 - Find the length of the arc of the curve from point...Ch. 8.1 - Find the length of the arc of the curve from point...Ch. 8.1 - Graph the curve and visually estimate its length....Ch. 8.1 - Graph the curve and visually estimate its length....Ch. 8.1 - Use Simpsons Rule with n=10 to estimate the arc...Ch. 8.1 - Use Simpsons Rule with n=10 to estimate the arc...Ch. 8.1 - Use Simpsons Rule with n=10 to estimate the arc...Ch. 8.1 - Use Simpsons Rule with n=10 to estimate the arc...Ch. 8.1 - a Graph the curve y=x4x3,0x4. b Compute the...Ch. 8.1 - Repeat Exercise 29 for the curve y=x+sinx 0x2Ch. 8.1 - Use either a computer algebra system or a table of...Ch. 8.1 - Use either a computer algebra system or a table of...Ch. 8.1 - Sketch the curve with equation x2/3+y2/3=1 and use...Ch. 8.1 - a Sketch the curve y3=x2. b Use Formulas 3 and 4...Ch. 8.1 - Find the arc length function for the curve y=2x3/2...Ch. 8.1 - a Find the arc length function for the curve...Ch. 8.1 - Find the arc length function for the curve...Ch. 8.1 - The arc length function for a curve y=f(x), where...Ch. 8.1 - For the function f(x)=14ex+ex, prove that the arc...Ch. 8.1 - A steady wind blows a kite due west. The kites...Ch. 8.1 - A hawk flying at 15 m/s at an altitude of 180 m...Ch. 8.1 - The Gateway Arch in St. Louis see the photo on...Ch. 8.1 - A manufacturer of corrugated metal roofing wants...Ch. 8.1 - a The figure shows a telephone wire hanging...Ch. 8.1 - Find the length of the curve y=1xt31dt1x4Ch. 8.1 - The curves with equations xn+yn=1, n=4,6,8,...,...Ch. 8.2 - a Set up an integral for the area of the surface...Ch. 8.2 - a Set up an integral for the area of the surface...Ch. 8.2 - a Set up an integral for the area of the surface...Ch. 8.2 - a Set up an integral for the area of the surface...Ch. 8.2 - a Set up an integral for the area of the surface...Ch. 8.2 - a Set up an integral for the area of the surface...Ch. 8.2 - Find the exact area of the surface obtained by...Ch. 8.2 - Find the exact area of the surface obtained by...Ch. 8.2 - Find the exact area of the surface obtained by...Ch. 8.2 - Find the exact area of the surface obtained by...Ch. 8.2 - Find the exact area of the surface obtained by...Ch. 8.2 - Find the exact area of the surface obtained by...Ch. 8.2 - Find the exact area of the surface obtained by...Ch. 8.2 - Find the exact area of the surface obtained by...Ch. 8.2 - The given curve is rotated about the y-axis. Find...Ch. 8.2 - The given curve is rotated about the y-axis. Find...Ch. 8.2 - The given curve is rotated about the y-axis. Find...Ch. 8.2 - The given curve is rotated about the y-axis. Find...Ch. 8.2 - Use Simpsons Rule with n = 10 to approximate the...Ch. 8.2 - Use Simpsons Rule with n = 10 to approximate the...Ch. 8.2 - Use Simpsons Rule with n = 10 to approximate the...Ch. 8.2 - Use Simpsons Rule with n = 10 to approximate the...Ch. 8.2 - Use either a CAS or a table of integrals to find...Ch. 8.2 - Use either a CAS or a table of integrals to find...Ch. 8.2 - Use a CAS to find the exact area of the surface...Ch. 8.2 - Use a CAS to find the exact area of the surface...Ch. 8.2 - If the region ={(x,y)x1,0y1/x} is rotated about...Ch. 8.2 - If the infinite curve y=ex,x0, is rotated about...Ch. 8.2 - a If a 0, find the area of the surface generated...Ch. 8.2 - A group of engineers is building a parabolic...Ch. 8.2 - a The ellipse x2a2+y2b2=1ab is rotated about the...Ch. 8.2 - Find the surface area of the torus in Exercise...Ch. 8.2 - If the curve y=f(x),axb, is rotated about the...Ch. 8.2 - Use the result of Exercise 33 to set up an...Ch. 8.2 - Find the area of the surface obtained by rotating...Ch. 8.2 - a Show that the surface area of a zone of a sphere...Ch. 8.2 - Show that if we rotate the curve y=ex/2+ex/2 about...Ch. 8.2 - Let L be the length of the curve y=f(x),axb, where...Ch. 8.2 - Formula 4 is valid only when f(x)0. Show that when...Ch. 8.3 - An aquarium 5 ft long, 2 ft wide, and 3 ft deep is...Ch. 8.3 - A tank is 8 m long, 4 m wide, 2 m high, and...Ch. 8.3 - A vertical plate is submerged or partially...Ch. 8.3 - A vertical plate is submerged or partially...Ch. 8.3 - A vertical plate is submerged or partially...Ch. 8.3 - A vertical plate is submerged or partially...Ch. 8.3 - A vertical plate is submerged or partially...Ch. 8.3 - A vertical plate is submerged or partially...Ch. 8.3 - A vertical plate is submerged or partially...Ch. 8.3 - A vertical plate is submerged or partially...Ch. 8.3 - A vertical plate is submerged or partially...Ch. 8.3 - A milk truck carries milk with density 64.6lb/ft3...Ch. 8.3 - A trough is filled with a liquid of density...Ch. 8.3 - A vertical dam has a semicircular gate as shown in...Ch. 8.3 - A cube with 20-cm-long sides is sitting on the...Ch. 8.3 - A dam is inclined at an angle of 30 from the...Ch. 8.3 - A swimming pool is 20 ft wide and 40 ft long and...Ch. 8.3 - Suppose that a plate is immersed vertically in a...Ch. 8.3 - A metal plate was found submerged vertically in...Ch. 8.3 - a Use the formula of Exercise 18 to show that...Ch. 8.3 - oint-masse mi are located on the x-axis as shown....Ch. 8.3 - oint-masse mi are located on the x-axis as shown....Ch. 8.3 - The masses mi are located at the points Pi. Find...Ch. 8.3 - The masses mi are located at the points Pi. Find...Ch. 8.3 - Sketch the region bounded by the curves, and...Ch. 8.3 - Sketch the region bounded by the curves, and...Ch. 8.3 - Sketch the region bounded by the curves, and...Ch. 8.3 - Sketch the region bounded by the curves, and...Ch. 8.3 - Find the centroid of the region bounded by the...Ch. 8.3 - Find the centroid of the region bounded by the...Ch. 8.3 - Find the centroid of the region bounded by the...Ch. 8.3 - Find the centroid of the region bounded by the...Ch. 8.3 - Find the centroid of the region bounded by the...Ch. 8.3 - Calculate the moments Mx and My and the center of...Ch. 8.3 - Calculate the moments Mx and My and the center of...Ch. 8.3 - Use Simpsons Rule to estimate the centroid of the...Ch. 8.3 - Find the centroid of the region bounded by the...Ch. 8.3 - Use a graph to find approximate x-coordinates of...Ch. 8.3 - Prove that the centroid of any triangle is located...Ch. 8.3 - Find the centroid of the region shown, not by...Ch. 8.3 - Find the centroid of the region shown, not by...Ch. 8.3 - A rectangle with sides a and b is divided into...Ch. 8.3 - If x is the x-coordinate of the centroid of the...Ch. 8.3 - Use the Theorem of Pappus to find the volume of...Ch. 8.3 - Use the Theorem of Pappus to find the volume of...Ch. 8.3 - Use the Theorem of Pappus to find the volume of...Ch. 8.3 - The centroid of a curve can be found by a process...Ch. 8.3 - The Second Theorem of Pappus is in the same spirit...Ch. 8.3 - Use the Second Theorem of Pappus described in...Ch. 8.3 - Let be the region that lies between the curves...Ch. 8.3 - Prove Formulas 9.Ch. 8.4 - The marginal cost function C(x) was defined to be...Ch. 8.4 - A company estimates that the marginal revenue in...Ch. 8.4 - A mining company estimates that the marginal cost...Ch. 8.4 - The demand functionjbr a particular vacation...Ch. 8.4 - A demand curve is given by p=450/(x+8). Find the...Ch. 8.4 - The supply function ps(x) for a commodity gives...Ch. 8.4 - If a supply curve is modeled by the equation...Ch. 8.4 - In a purely competitive market, the price of a...Ch. 8.4 - The sum of consumer surplus and producer surplus...Ch. 8.4 - A camera company estimates that the demand...Ch. 8.4 - A company modeled the demand curve for its product...Ch. 8.4 - A movie theater has been charging 10.00 per person...Ch. 8.4 - If the amount of capital that a company has at...Ch. 8.4 - If revenue flows into a company at a rate of...Ch. 8.4 - If income is continuously collected at a rate of...Ch. 8.4 - The present value of an income stream is the...Ch. 8.4 - Paretos Law of Income states that the number of...Ch. 8.4 - A hot, wet summer is causing a mosquito population...Ch. 8.4 - Use Poiseuilles Law to calculate the rate of flow...Ch. 8.4 - High blood pressure results from constriction of...Ch. 8.4 - The dye dilution method is used to measure cardiac...Ch. 8.4 - After a 5.5-mg injection of dye, the readings of...Ch. 8.4 - The graph of the concentration function c(t) is...Ch. 8.5 - Let f(x) be the probability density function for...Ch. 8.5 - Let f(t) be the probability density function for...Ch. 8.5 - Let f(x)=30x2(1x)2 for 0x1 and f(x)=0 all other...Ch. 8.5 - The density function f(x)=e3x(1+e3x)2 is an...Ch. 8.5 - Let f(x)=c/(1+x2). a For what value of c is f a...Ch. 8.5 - Let f(x)=k(3xx2) if 0x3 and f(x)=0 if x0 or x3. a...Ch. 8.5 - A spinner from a board game randomly indicates a...Ch. 8.5 - a Explain why the function whose graph is shown is...Ch. 8.5 - Show that the median waiting time for a phone call...Ch. 8.5 - a A type of fight bulb is labeled as having an...Ch. 8.5 - An online retailer has determined that the average...Ch. 8.5 - The time between infection and the display of...Ch. 8.5 - REM sleep is the phase of sleep when most active...Ch. 8.5 - According to the National Health Survey, the...Ch. 8.5 - The Garbage Project at the University of Arizona...Ch. 8.5 - Boxes are labeled as containing 500 g of cereal....Ch. 8.5 - The speeds of vehicles on a highway with speed...Ch. 8.5 - Show that the probability density function for a...Ch. 8.5 - For any normal distribution, find the probability...Ch. 8.5 - The standard deviation for a random variable with...Ch. 8.5 - The hydrogen atom is composed of one proton in the...Ch. 8.R - a How is the length of a curve defined? b Write an...Ch. 8.R - a Write an expression for the surface area of the...Ch. 8.R - Describe how we can find the hydrostatic force...Ch. 8.R - a What is the physical significance of the centre...Ch. 8.R - What does the Theorem of Pappus Say?Ch. 8.R - Given a demand function p(x), explain what is...Ch. 8.R - a What is the cardiac output of the heart? b...Ch. 8.R - What is a probability density function? What...Ch. 8.R - Suppose f(x) is the probability density function...Ch. 8.R - What is a normal distribution? What is the...Ch. 8.R - Find the length of the curve. y=4(x1)3/2,1x4Ch. 8.R - 13 Find the length of the curve. y=2...Ch. 8.R - 13 Find the length of the curve. 12x=4y3+3y1,1y3Ch. 8.R - a Find the length of the curve y=x416+12x21x2 b...Ch. 8.R - Let C be the arc of the curve y=2/(x+1) from the...Ch. 8.R - a The curve y=x2,0x1, is rotated about the y-axis....Ch. 8.R - Use Simpsons Rule with Simpsons Rule with n=10 to...Ch. 8.R - Use Simpsons Rule with Simpsons Rule with n=10 to...Ch. 8.R - Find the length of the curve y=1xt1dt1x16Ch. 8.R - Find the area of the surface obtained by rotating...Ch. 8.R - A gate in an irrigation canal is constructed in...Ch. 8.R - A trough is filled with water and its vertical...Ch. 8.R - 1314 Find the centroid of the region shown.Ch. 8.R - 1314 Find the centroid of the region shown.Ch. 8.R - 1516 Find the centroid of the region bounded by...Ch. 8.R - 1516 Find the centroid of the region bounded by...Ch. 8.R - Find the volume obtained when the circle of radius...Ch. 8.R - Use the Theorem of Pappus and the fact that the...Ch. 8.R - The demand function for a commodity is given by...Ch. 8.R - After a 6-mg injection of dye into a heart, the...Ch. 8.R - a Explain why the function...Ch. 8.R - Lengths of human pregnancies are normally...Ch. 8.R - The length of time spent waiting in line at a...Ch. 8.P - Find the area of the region...Ch. 8.P - Find the centroid of the region enclosed by the...Ch. 8.P - If a sphere of radius r is sliced by a plane whose...Ch. 8.P - a Show that an observer at height H above the...Ch. 8.P - Suppose that the density of seawater, =(z), varies...Ch. 8.P - The figure shows a semicircle with radius 1,...Ch. 8.P - Let P be a pyramid with a square base of side 2b...Ch. 8.P - Consider a flat metal plate to be placed...Ch. 8.P - A uniform disk with radius 1 m is to be cut by a...Ch. 8.P - A triangle with area 30cm2 is cut from a corner of...Ch. 8.P - In a famous 18th-century problem, known as Buffons...Ch. 8.P - If the needle in Problem 11 has length hL, its...Ch. 8.P - Find the centroid of the region enclosed by the...

Additional Math Textbook Solutions

Find more solutions based on key concepts
Show solutions
Add or Subtract Perform the addition or subtraction and simplify. 1x+3+1x29

Precalculus: Mathematics for Calculus (Standalone Book)

Birthrate of Endangered Species The birthrate of an endangered species of whales in year t is f(t) whales/year....

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

A=12bh,b=40,andh=15,findA

Elementary Technical Mathematics

True or False: In general, better approximations to the area under the curve y = f(x) between x = a and x = b a...

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Prove: If ab=cd where a, b, c and d are nonzero, then ac=bd.

Elementary Geometry for College Students

Graph each function by using transformations. fx=3x+1

College Algebra (MindTap Course List)

Consider a sample with data values of 10, 20, 12, 17, and 16. Compute the mean and median.

Statistics for Business & Economics, Revised (MindTap Course List)

Reminder Round all answers to two decimal places unless otherwise indicated. Probability of ExtinctionAn expone...

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

46. After deducting grants based on need, the average cost to attend the University of Southern California (USC...

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)

In Problems 112 find the general solution of the given system. 6. X=(6231)X

A First Course in Differential Equations with Modeling Applications (MindTap Course List)