 6.1: Calculate the following integrals. ?32dx
 6.2: Calculate the following integrals. ?(x23x+2)dx
 6.3: Calculate the following integrals. ?x+1dx
 6.4: Calculate the following integrals. ?2x+4dx
 6.5: Calculate the following integrals. 2?(x3+3x21)dx
 6.6: Calculate the following integrals. ?5x+3dx
 6.7: Calculate the following integrals. ?ex/2dx
 6.8: Calculate the following integrals. ?5x7dx
 6.9: Calculate the following integrals. ?(3x44x3)dx
 6.10: Calculate the following integrals. ? 2x+3)7dx
 6.11: Calculate the following integrals. ?4xdx
 6.12: Calculate the following integrals. ?5xx5dx
 6.13: Calculate the following integrals. ?11(x+1)2dx
 6.14: Calculate the following integrals. ?1/803xdx
 6.15: Calculate the following integrals. ?212x+4dx
 6.16: Calculate the following integrals. 2?102x+11x+4dx
 6.17: Calculate the following integrals. ?214x5dx
 6.18: Calculate the following integrals. 23?80x+1dx
 6.19: Calculate the following integrals. ?411x2dx
 6.20: Calculate the following integrals. ?63e2(x/3)dx
 6.21: Calculate the following integrals. ?50(5 + 3x)1dx
 6.22: Calculate the following integrals? 232e3xdx
 6.23: Calculate the following integrals. ?ln 20(exex)dx
 6.24: Calculate the following integrals. ?ln 3ln 2(ex+ex)dx
 6.25: Calculate the following integrals. ?ln 30ex+exe2xdx
 6.26: Calculate the following integrals. ?103+e2xexdx
 6.27: Calculate the following integrals. Find the area under the curvey=(...
 6.28: Calculate the following integrals. Find the area under the curvey=1...
 6.29: find the area of the shaded region. y = x2yx01y = x
 6.30: find the area of the shaded region. y = x3yx022y =x3 + 2x12
 6.31: find the area of the shaded region. y = exy = exyx011ln 2
 6.32: find the area of the shaded region. y = x2yx01.21y = x
 6.33: find the area of the shaded region. y = 4 x2y = 1 x2yx04112
 6.34: find the area of the shaded region. y = 1 1/xyx0121/2xy = x2 3212
 6.35: find the area of the shaded region. y = exexyx01
 6.36: find the area of the shaded region. 2y = x3yx03y = 2x3x2 6x
 6.37: Find the area of the region bounded by the curvesy=x33x+1 andy=x+1.
 6.38: Find the area of the region between the curvesy=2x2+xandy=x2+2 from...
 6.39: Find the functionf(x)forwhichf?(x)=(x5)2,f(8) = 2.
 6.40: Find the functionf(x)forwhichf( ? x)=e5x,f(0) = 1.
 6.41: Describe all solutions of the following differential equations, wh...
 6.42: Letkbe a constant, and lety=f(t) be a function suchthaty?=kty. Show...
 6.43: An airplane tire plant finds that its marginal cost of producing t...
 6.44: If the marginal revenue function for a company is4003x2, find the a...
 6.45: A drug is injected into a patient at the rate off(t)cubic centimet...
 6.46: A rock thrown straight up into the air has a velocity ofv(t)=9.8t+ ...
 6.47: Use a Riemann sum withn= 4 and left endpoints to estimate the area...
 6.48: Redo Exercise 47 using right endpoints.
 6.49: Use a Riemann sum withn= 2 and midpoints to estimatethe area under ...
 6.50: Use a Riemann sum withn= 5 and midpoints to estimate the area unde...
 6.51: Find the consumers surplus for the demand curvep=25.04xat the sales...
 6.52: Three thousand dollars is deposited in the bank at 4%interest compo...
 6.53: Find the average value off(x)=1/x3fromx=13tox=12.
 6.54: Suppose that the interval 0x1 is divided into 100subintervals with ...
 6.55: In Fig. 2, three regions are labeled with their areas. Determine?c...
 6.56: Find the volume of the solid of revolution generated byrevolving ab...
 6.57: A store has an inventory ofQunits of a certain productat timet= 0. ...
 6.58: A retail store sells a certain product at the rate ofg(t)units per ...
 6.59: Letxbe any positive number, and defineg(x)tobethenumber determined ...
 6.60: For each numb erxsatisfying1x1, defineh(x)byh(x)=?x11t2dt.(a)Give a...
 6.61: Suppose that the interval 0t3 is divided into 1000subintervals of w...
 6.62: What number does?e0+e1/n+e2/n+e3/n++e(n1)/n?1napproach asngets very...
 6.63: What number does the sum?13+1+1n3+1+2n3+1+3n3++1+n1n3?1napproach as...
 6.64: In Fig. 3, the rectangle has the same area as the regionunder the g...
 6.65: True or false:If3f(x)4 whenever 0x5, then315?50f(x)dx4.
 6.66: Suppose that water is flowing into a tank at a rate ofr(t)gallons p...
 6.67: The annual world rate of water usetyears after 1960, fort35, was ap...
 6.68: If money is deposited steadily in a savings account at therate of $...
 6.69: Find a functionf(x) whose graph goes through thepoint (1,1) and who...
 6.70: For what value ofais the shaded area in Fig. 4 equalto 1?y = x2(a, ...
 6.71: Show that for any positive numberbwe have?b20xdx+?b0x2dx=b3.
 6.72: Generalize the result of Exercise 71 as follows: Letnbe apositive i...
 6.73: Show that1? 0(xx2)dx=13.
 6.74: Generalize the result of Exercise 73 as follows: Letnbe apositive i...
Solutions for Chapter 6: Calculus with Applications 13th Edition
Full solutions for Calculus with Applications  13th Edition
ISBN: 9780321848901
Solutions for Chapter 6
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Since 74 problems in chapter 6 have been answered, more than 3507 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Calculus with Applications, edition: 13. Chapter 6 includes 74 full stepbystep solutions. Calculus with Applications was written by and is associated to the ISBN: 9780321848901.

Absolute value of a vector
See Magnitude of a vector.

Basic logistic function
The function ƒ(x) = 1 / 1 + ex

Common difference
See Arithmetic sequence.

Conversion factor
A ratio equal to 1, used for unit conversion

Coterminal angles
Two angles having the same initial side and the same terminal side

Doubleangle identity
An identity involving a trigonometric function of 2u

Identity matrix
A square matrix with 1’s in the main diagonal and 0’s elsewhere, p. 534.

Implicitly defined function
A function that is a subset of a relation defined by an equation in x and y.

Inverse secant function
The function y = sec1 x

Lower bound for real zeros
A number c is a lower bound for the set of real zeros of ƒ if ƒ(x) Z 0 whenever x < c

n factorial
For any positive integer n, n factorial is n! = n.(n  1) . (n  2) .... .3.2.1; zero factorial is 0! = 1

Natural exponential function
The function ƒ1x2 = ex.

Normal curve
The graph of ƒ(x) = ex2/2

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

Pascal’s triangle
A number pattern in which row n (beginning with n = 02) consists of the coefficients of the expanded form of (a+b)n.

Present value of an annuity T
he net amount of your money put into an annuity.

Probability distribution
The collection of probabilities of outcomes in a sample space assigned by a probability function.

Rigid transformation
A transformation that leaves the basic shape of a graph unchanged.

Time plot
A line graph in which time is measured on the horizontal axis.

Weights
See Weighted mean.