 5.1: (a) Write an expression for a Riemann sum of a function f. Explain ...
 5.2: (a) Write the definition of the definite integral of a continuous f...
 5.3: State the Midpoint Rule.
 5.4: State both parts of the Fundamental Theorem of Calculus.
 5.5: (a) State the Net Change Theorem. (b) If rstd is the rate at which ...
 5.6: Suppose a particle moves back and forth along a straight line with ...
 5.7: (a) Explain the meaning of the indefinite integral y fsxd dx. (b) W...
 5.8: Explain exactly what is meant by the statement that differentiation...
 5.9: State the Substitution Rule. In practice, how do you use it?
 5.10: Determine whether the statement is true or false. If it is true, ex...
 5.11: Determine whether the statement is true or false. If it is true, ex...
 5.12: Determine whether the statement is true or false. If it is true, ex...
 5.13: Determine whether the statement is true or false. If it is true, ex...
 5.14: Determine whether the statement is true or false. If it is true, ex...
 5.15: Determine whether the statement is true or false. If it is true, ex...
 5.16: Determine whether the statement is true or false. If it is true, ex...
 5.17: Determine whether the statement is true or false. If it is true, ex...
 5.18: Determine whether the statement is true or false. If it is true, ex...
 5.19: Evaluate the integral, if it exists. y 5 1 dt st 2 4d 2
 5.20: Evaluate the integral, if it exists. y 1 0 sins3td dt
 5.21: Evaluate the integral, if it exists. y 1 0 v2 cossv3 d dv
 5.22: Evaluate the integral, if it exists. y 1 21 sin x 1 1 x 2 dx
 5.23: Evaluate the integral, if it exists. y y4 2y4 t 4 tan t 2 1 cos t dt
 5.24: Evaluate the integral, if it exists. y 1 0 ex 1 1 e 2x dx
 5.25: Evaluate the integral, if it exists. y S 1 2 x x D 2 dx
 5.26: Evaluate the integral, if it exists. y 10 1 x x 2 2 4 dx
 5.27: Evaluate the integral, if it exists. y x 1 2 sx 2 1 4x dx
 5.28: Evaluate the integral, if it exists. y csc2 x 1 1 cot x dx
 5.29: Evaluate the integral, if it exists. y sin t cos t dt
 5.30: Evaluate the integral, if it exists. y sin x cosscos xd dx
 5.31: Evaluate the integral, if it exists. y esx sx dx
 5.32: Evaluate the integral, if it exists. y sinsln xd x dx
 5.33: Evaluate the integral, if it exists.y tan x lnscos xd dx
 5.34: Evaluate the integral, if it exists. y x s1 2 x 4 dx
 5.35: Evaluate the integral, if it exists.y x 3 1 1 x 4 dx
 5.36: Evaluate the integral, if it exists. y sinhs1 1 4xd dx
 5.37: Evaluate the integral, if it exists. y sec tan 1 1 sec d
 5.38: Evaluate the integral, if it exists.y y4 0 s1 1 tan td 3 sec2 t dt
 5.39: Evaluate the integral, if it exists. y 3 0  x 2 2 4  dx
 5.40: Evaluate the integral, if it exists. y 4 0  sx 2 1  dx
 5.41: Evaluate the indefinite integral. Illustrate and check that your an...
 5.42: Evaluate the indefinite integral. Illustrate and check that your an...
 5.43: Use a graph to give a rough estimate of the area of the region that...
 5.44: Graph the function fsxd cos2 x sin x and use the graph to guess the...
 5.45: Find the derivative of the function Fsxd y x 0 t 2 1 1 t 3 dt
 5.46: Find the derivative of the function Fsxd y 1 x st 1 sin t dt
 5.47: Find the derivative of the function tsxd y x4 0 cosst 2 d dt
 5.48: Find the derivative of the function tsxd y sin x 1 1 2 t 2 1 1 t 4 dt
 5.49: Find the derivative of the function . y y x sx et t dt
 5.50: Find the derivative of the function y y 3x11 2x sinst 4 d dt
 5.51: Use Property 8 of integrals to estimate the value of the integral. ...
 5.52: Use Property 8 of integrals to estimate the value of the integral. ...
 5.53: Use the properties of integrals to verify the inequality. y 1 0 x 2...
 5.54: Use the properties of integrals to verify the inequality. y y2 y4 s...
 5.55: Use the properties of integrals to verify the inequality. y 1 0 ex ...
 5.56: Use the properties of integrals to verify the inequality. y 1 0 x s...
 5.57: Use the Midpoint Rule with n 6 to approximate y 3 0 sinsx 3 d dx.
 5.58: A particle moves along a line with velocity function vstd t 2 2 t, ...
 5.59: Let rstd be the rate at which the worlds oil is consumed, where t i...
 5.60: A radar gun was used to record the speed of a runner at the times g...
 5.61: A population of honeybees increased at a rate of rstd bees per week...
 5.62: . Let fsxd H 2x 2 1 2s1 2 x 2 if 23 < x < 0 if 0 < x < 1 Evaluate y...
 5.63: If f is continuous and y 2 0 fsxd dx 6, evaluate y y2 0 fs2 sin d c...
 5.64: The Fresnel function Ssxd y x 0 sin(1 2t 2 ) dt was introduced in S...
 5.65: Estimate the value of the number c such that the area under the cur...
 5.66: Suppose that the temperature in a long, thin rod placed along the x...
 5.67: If f is a continuous function such that y x 1 fstd dt sx 2 1de 2x 1...
 5.68: Suppose h is a function such that hs1d 22, h9s1d 2, h0s1d 3, hs2d 6...
 5.69: If f9 is continuous on fa, bg, show that 2 y b a fsxd f9sxd dx f fs...
 5.70: Find lim hl0 1 h y 21h 2 s1 1 t 3 dt
 5.71: If f is continuous on f0, 1g, prove that y 1 0 fsxd dx y 1 0 fs1 2 ...
 5.72: Evaluate lim n l` 1 n FS 1 n D 9 1 S 2 n D 9 1 S 3 n D 9 1 1 S n n ...
 5.73: Suppose f is continuous, fs0d 0, fs1d 1, f9sxd . 0, and y 1 0 fsxd ...
Solutions for Chapter 5: Integrals
Full solutions for Single Variable Calculus: Early Transcendentals  8th Edition
ISBN: 9781305270336
Solutions for Chapter 5: Integrals
Get Full SolutionsThis textbook survival guide was created for the textbook: Single Variable Calculus: Early Transcendentals, edition: 8. This expansive textbook survival guide covers the following chapters and their solutions. Single Variable Calculus: Early Transcendentals was written by and is associated to the ISBN: 9781305270336. Chapter 5: Integrals includes 73 full stepbystep solutions. Since 73 problems in chapter 5: Integrals have been answered, more than 38148 students have viewed full stepbystep solutions from this chapter.

Common logarithm
A logarithm with base 10.

Direction of an arrow
The angle the arrow makes with the positive xaxis

End behavior asymptote of a rational function
A polynomial that the function approaches as.

Equivalent vectors
Vectors with the same magnitude and direction.

Exponential form
An equation written with exponents instead of logarithms.

Fibonacci numbers
The terms of the Fibonacci sequence.

Finite sequence
A function whose domain is the first n positive integers for some fixed integer n.

Hyperboloid of revolution
A surface generated by rotating a hyperbola about its transverse axis, p. 607.

Logarithmic function with base b
The inverse of the exponential function y = bx, denoted by y = logb x

Nautical mile
Length of 1 minute of arc along the Earth’s equator.

Negative numbers
Real numbers shown to the left of the origin on a number line.

nth root of unity
A complex number v such that vn = 1

Orthogonal vectors
Two vectors u and v with u x v = 0.

Polar form of a complex number
See Trigonometric form of a complex number.

Positive angle
Angle generated by a counterclockwise rotation.

Right angle
A 90° angle.

Sphere
A set of points in Cartesian space equally distant from a fixed point called the center.

Term of a polynomial (function)
An expression of the form anxn in a polynomial (function).

Upper bound for ƒ
Any number B for which ƒ(x) ? B for all x in the domain of ƒ.

Weighted mean
A mean calculated in such a way that some elements of the data set have higher weights (that is, are counted more strongly in determining the mean) than others.