8th Edition

ISBN: 9781285740621

Author: James Stewart

Publisher: Cengage Learning

Concept explainers

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

Textbook Question

Chapter 8.3, Problem 1E

An aquarium 5 ft long, 2 ft wide, and 3 ft deep is full of water. Find (a) the hydrostatic pressure on the bottom of the aquarium, (b) the hydrostatic force on the bottom, and (c) the hydrostatic force on one end of the aquarium.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8.2, Problem 39E

Chapter 8.3, Problem 2E

Chapter 8 Solutions

Calculus (MindTap Course List)

Ch. 8.1 - Use the arc length formula 3 to find the length of...Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E Ch. 8.1 - Prob. 8E Ch. 8.1 - Find the exact length of the curve. y=1+6x3/2, 0x1 Ch. 8.1 - Prob. 10E

Ch. 8.1 - Find the exact length of the curve. y=x33+14x,1x2 Ch. 8.1 - Find the exact length of the curve. x=y48+14y2,1y2 Ch. 8.1 - Find the exact length of the curve. x=13y(y3),1y9 Ch. 8.1 - Find the exact length of the curve....Ch. 8.1 - Find the exact length of the curve....Ch. 8.1 - Prob. 16E Ch. 8.1 - Find the exact length of the curve....Ch. 8.1 - Prob. 18E Ch. 8.1 - Find the exact length of the curve. y=ln(1x2),0x12 Ch. 8.1 - Prob. 20E Ch. 8.1 - Prob. 21E Ch. 8.1 - Prob. 22E Ch. 8.1 - Prob. 23E Ch. 8.1 - Prob. 24E 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 0x2 Ch. 8.1 - Prob. 31E Ch. 8.1 - Prob. 32E Ch. 8.1 - Prob. 33E Ch. 8.1 - a Sketch the curve y3=x2. b Use Formulas 3 and 4...Ch. 8.1 - Prob. 35E Ch. 8.1 - Prob. 36E Ch. 8.1 - Prob. 37E 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 - Prob. 40E Ch. 8.1 - A hawk flying at 15 m/s at an altitude of 180 m...Ch. 8.1 - Prob. 42E Ch. 8.1 - Prob. 43E Ch. 8.1 - a The figure shows a telephone wire hanging...Ch. 8.1 - Prob. 45E Ch. 8.1 - Prob. 46E Ch. 8.2 - a Set up an integral for the area of the surface...Ch. 8.2 - Prob. 2E Ch. 8.2 - Prob. 3E Ch. 8.2 - Prob. 4E 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 - Prob. 10E Ch. 8.2 - Find the exact area of the surface obtained by...Ch. 8.2 - Prob. 12E Ch. 8.2 - Find the exact area of the surface obtained by...Ch. 8.2 - Prob. 14E 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 - Prob. 18E Ch. 8.2 - Prob. 19E Ch. 8.2 - Prob. 20E 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 - Prob. 23E Ch. 8.2 - Prob. 24E Ch. 8.2 - Prob. 25E Ch. 8.2 - Prob. 26E 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 - Prob. 29E 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 - Prob. 33E Ch. 8.2 - Prob. 34E 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 - Prob. 38E 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 - Prob. 3E Ch. 8.3 - A vertical plate is submerged or partially...Ch. 8.3 - A vertical plate is submerged or partially...Ch. 8.3 - Prob. 6E 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 - Prob. 10E Ch. 8.3 - Prob. 11E 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 - Prob. 16E Ch. 8.3 - A swimming pool is 20 ft wide and 40 ft long and...Ch. 8.3 - Prob. 18E Ch. 8.3 - Prob. 19E Ch. 8.3 - Prob. 20E Ch. 8.3 - Prob. 21E Ch. 8.3 - Prob. 22E Ch. 8.3 - Prob. 23E Ch. 8.3 - Prob. 24E Ch. 8.3 - Prob. 25E 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 - Prob. 28E Ch. 8.3 - Prob. 29E Ch. 8.3 - Prob. 30E Ch. 8.3 - Prob. 31E 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 - Prob. 36E Ch. 8.3 - Prob. 37E Ch. 8.3 - Prob. 38E 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 - Prob. 43E Ch. 8.3 - Prob. 44E 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 - Prob. 48E Ch. 8.3 - Prob. 49E Ch. 8.3 - Prob. 50E Ch. 8.3 - Prob. 51E Ch. 8.4 - The marginal cost function C(x) was defined to be...Ch. 8.4 - Prob. 2E Ch. 8.4 - Prob. 3E Ch. 8.4 - Prob. 4E Ch. 8.4 - Prob. 5E Ch. 8.4 - The supply function ps(x) for a commodity gives...Ch. 8.4 - Prob. 7E Ch. 8.4 - Prob. 8E Ch. 8.4 - Prob. 9E Ch. 8.4 - A camera company estimates that the demand...Ch. 8.4 - Prob. 11E Ch. 8.4 - Prob. 12E Ch. 8.4 - Prob. 13E Ch. 8.4 - Prob. 14E Ch. 8.4 - Prob. 15E Ch. 8.4 - Prob. 16E Ch. 8.4 - Prob. 17E Ch. 8.4 - A hot, wet summer is causing a mosquito population...Ch. 8.4 - Prob. 19E Ch. 8.4 - Prob. 20E Ch. 8.4 - The dye dilution method is used to measure cardiac...Ch. 8.4 - Prob. 22E Ch. 8.4 - The graph of the concentration function c(t) is...Ch. 8.5 - Prob. 1E Ch. 8.5 - Prob. 2E Ch. 8.5 - Prob. 3E Ch. 8.5 - Prob. 4E Ch. 8.5 - Let f(x)=c/(1+x2). a For what value of c is f a...Ch. 8.5 - Prob. 6E Ch. 8.5 - Prob. 7E 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 - Prob. 10E 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 - Prob. 13E Ch. 8.5 - Prob. 14E Ch. 8.5 - Prob. 15E Ch. 8.5 - Prob. 16E Ch. 8.5 - The speeds of vehicles on a highway with speed...Ch. 8.5 - Prob. 18E Ch. 8.5 - For any normal distribution, find the probability...Ch. 8.5 - Prob. 20E Ch. 8.5 - The hydrogen atom is composed of one proton in the...Ch. 8.R - Prob. 1CC Ch. 8.R - Prob. 2CC Ch. 8.R - Prob. 3CC Ch. 8.R - a What is the physical significance of the centre...Ch. 8.R - Prob. 5CC Ch. 8.R - Prob. 6CC Ch. 8.R - Prob. 7CC Ch. 8.R - Prob. 8CC Ch. 8.R - Prob. 9CC Ch. 8.R - Prob. 10CC Ch. 8.R - Prob. 1E Ch. 8.R - Prob. 2E Ch. 8.R - Prob. 3E Ch. 8.R - a Find the length of the curve y=x416+12x21x2 b...Ch. 8.R - Prob. 5E Ch. 8.R - Prob. 6E Ch. 8.R - Prob. 7E Ch. 8.R - Prob. 8E Ch. 8.R - Prob. 9E Ch. 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 - Prob. 13E Ch. 8.R - 1314 Find the centroid of the region shown.Ch. 8.R - Prob. 15E Ch. 8.R - Prob. 16E Ch. 8.R - Prob. 17E Ch. 8.R - Prob. 18E Ch. 8.R - Prob. 19E Ch. 8.R - Prob. 20E Ch. 8.R - Prob. 21E 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 - Prob. 5P Ch. 8.P - The figure shows a semicircle with radius 1,...Ch. 8.P - Prob. 7P Ch. 8.P - Consider a flat metal plate to be placed...Ch. 8.P - Prob. 9P Ch. 8.P - A triangle with area 30cm2 is cut from a corner of...Ch. 8.P - Prob. 11P Ch. 8.P - If the needle in Problem 11 has length hL, its...Ch. 8.P - Prob. 13P

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.