 5.5.1: The accompanying figure shows the graph of the velocity (fr/sec) of...
 5.5.2: a. The accompanying figure shows the velocity (mj sec) of a body mo...
 5.5.3: Suppose that ~ak = 2 and ~bk = 25. Find the value of iI iI 10 b....
 5.5.4: Suppose that ~ak = 0 and ~bk = 7. Find the values of 20 a. ~3ak k ...
 5.5.5: In Exercises 58, express each limit as a defutire inregral. Then e...
 5.5.6: In Exercises 58, express each limit as a defutire inregral. Then e...
 5.5.7: In Exercises 58, express each limit as a defutire inregral. Then e...
 5.5.8: In Exercises 58, express each limit as a defutire inregral. Then e...
 5.5.9: If t, 3f(x) dx = 12, f~,f(x) dx = 6, and f~,g(x) dx = 2, fmd the va...
 5.5.10: If fo'f(x)dx = 'IT, fo'7g(x)dx = 7, and 101 g(x)dx = 2, fmd the val...
 5.5.11: In Exercises 1114, rmd the total area of the region between the gr...
 5.5.12: In Exercises 1114, rmd the total area of the region between the gr...
 5.5.13: In Exercises 1114, rmd the total area of the region between the gr...
 5.5.14: In Exercises 1114, rmd the total area of the region between the gr...
 5.5.15: Find the areas of the regioos enclosed by the curves aod lines in E...
 5.5.16: Find the areas of the regioos enclosed by the curves aod lines in E...
 5.5.17: Find the areas of the regioos enclosed by the curves aod lines in E...
 5.5.18: Find the areas of the regioos enclosed by the curves aod lines in E...
 5.5.19: Find the areas of the regioos enclosed by the curves aod lines in E...
 5.5.20: Find the areas of the regioos enclosed by the curves aod lines in E...
 5.5.21: Find the areas of the regioos enclosed by the curves aod lines in E...
 5.5.22: Find the areas of the regioos enclosed by the curves aod lines in E...
 5.5.23: Find the areas of the regioos enclosed by the curves aod lines in E...
 5.5.24: Find the areas of the regioos enclosed by the curves aod lines in E...
 5.5.25: Find the areas of the regioos enclosed by the curves aod lines in E...
 5.5.26: Find the areas of the regioos enclosed by the curves aod lines in E...
 5.5.27: Find the area of the ''triangular'' regioo bounded 00 the left by x...
 5.5.28: Find the area of the ''triangular'' regioo bounded 00 the left by y...
 5.5.29: Find the extren3e values of f(x) ~ x'  3x2 and rmd the area of the...
 5.5.30: Find the area of the regioo cut frOO3 the rlrst quadrant by the cur...
 5.5.31: Find the total area of the region enclosed by the curve x ~ y2/3 ao...
 5.5.32: Find the total area of the regioo between the curves y ~ sin x aod ...
 5.5.33: Show that y ~ x 2 + l' + dl solves the initial value problen3 d'y I...
 5.5.34: Show that y ~ J;( I + 2v.;.;t) dl solves the initial value problem ...
 5.5.35: Express the solutions of the initial value probleD3S in Exercises 3...
 5.5.36: Express the solutions of the initial value probleD3S in Exercises 3...
 5.5.37: Evaluate the integrals in Exercises 3744. 2(COSX)'I/2 sinx dx
 5.5.38: Evaluate the integrals in Exercises 3744. (lJlnxr'/2 sec2 x dx
 5.5.39: Evaluate the integrals in Exercises 3744. /(28 + I + 2 cos (28 + l...
 5.5.40: Evaluate the integrals in Exercises 3744. (~ + 2 sec2 (28  'If)) d8
 5.5.41: Evaluate the integrals in Exercises 3744. / (I t) (I + t) dl
 5.5.42: Evaluate the integrals in Exercises 3744. (I + ~~2  I dl
 5.5.43: Evaluate the integrals in Exercises 3744. VI sin (21'/2) dl
 5.5.44: Evaluate the integrals in Exercises 3744. sec 8 IJln 8 VI + sec 8 d8
 5.5.45: Evaluate the integrals in Exercises 4570 1'<3X2  4x + 7) dx
 5.5.46: Evaluate the integrals in Exercises 4570 {I (88'  1182 + 5) dx
 5.5.47: Evaluate the integrals in Exercises 4570 Jl if dv
 5.5.48: Evaluate the integrals in Exercises 4570 Jl X<13 dx
 5.5.49: Evaluate the integrals in Exercises 4570 Jl IVI
 5.5.50: Evaluate the integrals in Exercises 4570 l' (I + VU)I/250. .r du
 5.5.51: Evaluate the integrals in Exercises 4570 ],1 0 (18 + I)'
 5.5.52: Evaluate the integrals in Exercises 4570 ],1 d7 0 V'(7  57)2
 5.5.53: Evaluate the integrals in Exercises 4570 {' x1/3(1  x2/3)'/2 dx
 5.5.54: Evaluate the integrals in Exercises 4570 Jo x'(i + 9x')"/2 dx
 5.5.55: Evaluate the integrals in Exercises 4570 ],,,,. 8in2 5r dr
 5.5.56: Evaluate the integrals in Exercises 4570 ],w/. cos2 (41  f) dl
 5.5.57: Evaluate the integrals in Exercises 4570 Jo see> 8 d8 csc2 x dx
 5.5.58: Evaluate the integrals in Exercises 4570
 5.5.59: Evaluate the integrals in Exercises 4570 w cot' ~ dx
 5.5.60: Evaluate the integrals in Exercises 4570 1Jln2~d8
 5.5.61: Evaluate the integrals in Exercises 4570 10secxtanxdx
 5.5.62: Evaluate the integrals in Exercises 4570 w/
 5.5.63: Evaluate the integrals in Exercises 4570 0 5(sinx!'/2cosxdx
 5.5.64: Evaluate the integrals in Exercises 4570
 5.5.65: Evaluate the integrals in Exercises 4570 15 sin' 3x cos 3x dx
 5.5.66: Evaluate the integrals in Exercises 4570
 5.5.67: Evaluate the integrals in Exercises 4570 /../2 3 .o VI+3sin'x
 5.5.68: Evaluate the integrals in Exercises 4570
 5.5.69: Evaluate the integrals in Exercises 4570 /.. /3o V2sec8
 5.5.70: Evaluate the integrals in Exercises 4570
 5.5.71: Find the average value of I(x) = nu: + b L over [I, 1] b. over [k...
 5.5.72: Find the average value of L Y = v'h over [0, 3] b. y= ~aver[O,a]
 5.5.73: Let I be a function that is differentiable on [a, b]. In Cbapter 2 ...
 5.5.74: Is it true that the average value of an integrable function over an...
 5.5.75: Compute the average value of the temperature function I(x) = 37 sin...
 5.5.76: Specific heat Cv is the amount of beat required to raise the temper...
 5.5.77: In Exercises 7780, fmddy/dx = 1% V2 + cos'ldl
 5.5.78: In Exercises 7780, fmddy/dx Y = J, V2 + cos'ldl
 5.5.79: In Exercises 7780, fmddy/dx y=   .dl
 5.5.80: In Exercises 7780, fmddy/dx Y = , dl
 5.5.81: Is it true that every function y = I(x) that is differentiable on [...
 5.5.82: Suppose that F(x) is an antiderivative of I(x) = v'1+7. Express 101...
 5.5.83: Find dy/dx if Y = !.' "\I1+I2 dl. Explain the main steps in yom cal...
 5.5.84: Find dy/dx if Y = t,.% (1/(1  I' dt. Explain the main steps in you...
 5.5.85: To meet the demand for parlcing, your town bas allocated the area s...
 5.5.86: Skydivers A and B are in a helicopter hovering at 6400 ft. Skydiver...
Solutions for Chapter 5: Integration
Full solutions for Thomas' Calculus  12th Edition
ISBN: 9780321587992
Solutions for Chapter 5: Integration
Get Full SolutionsSince 86 problems in chapter 5: Integration have been answered, more than 8634 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 5: Integration includes 86 full stepbystep solutions. This textbook survival guide was created for the textbook: Thomas' Calculus, edition: 12. Thomas' Calculus was written by and is associated to the ISBN: 9780321587992.

Absolute minimum
A value ƒ(c) is an absolute minimum value of ƒ if ƒ(c) ? ƒ(x)for all x in the domain of ƒ.

Arc length formula
The length of an arc in a circle of radius r intercepted by a central angle of u radians is s = r u.

Center
The central point in a circle, ellipse, hyperbola, or sphere

Empty set
A set with no elements

Leastsquares line
See Linear regression line.

Linear inequality in two variables x and y
An inequality that can be written in one of the following forms: y 6 mx + b, y … mx + b, y 7 mx + b, or y Ú mx + b with m Z 0

Matrix, m x n
A rectangular array of m rows and n columns of real numbers

Multiplicative inverse of a matrix
See Inverse of a matrix

nth root
See Principal nth root

Obtuse triangle
A triangle in which one angle is greater than 90°.

Order of magnitude (of n)
log n.

Parameter
See Parametric equations.

Quotient of complex numbers
a + bi c + di = ac + bd c2 + d2 + bc  ad c2 + d2 i

Quotient polynomial
See Division algorithm for polynomials.

Random numbers
Numbers that can be used by researchers to simulate randomness in scientific studies (they are usually obtained from lengthy tables of decimal digits that have been generated by verifiably random natural phenomena).

Solution of a system in two variables
An ordered pair of real numbers that satisfies all of the equations or inequalities in the system

Supply curve
p = ƒ(x), where x represents production and p represents price

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.

Xmax
The xvalue of the right side of the viewing window,.

Ymax
The yvalue of the top of the viewing window.