 4.5.1: In Exercises 16, complete the table by identifying and for the inte...
 4.5.2: In Exercises 16, complete the table by identifying and for the inte...
 4.5.3: In Exercises 16, complete the table by identifying and for the inte...
 4.5.4: In Exercises 16, complete the table by identifying and for the inte...
 4.5.5: In Exercises 16, complete the table by identifying and for the inte...
 4.5.6: In Exercises 16, complete the table by identifying and for the inte...
 4.5.7: In Exercises 734, find the indefinite integral and check the result...
 4.5.8: In Exercises 734, find the indefinite integral and check the result...
 4.5.9: In Exercises 734, find the indefinite integral and check the result...
 4.5.10: In Exercises 734, find the indefinite integral and check the result...
 4.5.11: In Exercises 734, find the indefinite integral and check the result...
 4.5.12: In Exercises 734, find the indefinite integral and check the result...
 4.5.13: In Exercises 734, find the indefinite integral and check the result...
 4.5.14: In Exercises 734, find the indefinite integral and check the result...
 4.5.15: In Exercises 734, find the indefinite integral and check the result...
 4.5.16: In Exercises 734, find the indefinite integral and check the result...
 4.5.17: In Exercises 734, find the indefinite integral and check the result...
 4.5.18: In Exercises 734, find the indefinite integral and check the result...
 4.5.19: In Exercises 734, find the indefinite integral and check the result...
 4.5.20: In Exercises 734, find the indefinite integral and check the result...
 4.5.21: In Exercises 734, find the indefinite integral and check the result...
 4.5.22: In Exercises 734, find the indefinite integral and check the result...
 4.5.23: In Exercises 734, find the indefinite integral and check the result...
 4.5.24: In Exercises 734, find the indefinite integral and check the result...
 4.5.25: In Exercises 734, find the indefinite integral and check the result...
 4.5.26: In Exercises 734, find the indefinite integral and check the result...
 4.5.27: In Exercises 734, find the indefinite integral and check the result...
 4.5.28: In Exercises 734, find the indefinite integral and check the result...
 4.5.29: In Exercises 734, find the indefinite integral and check the result...
 4.5.30: In Exercises 734, find the indefinite integral and check the result...
 4.5.31: In Exercises 734, find the indefinite integral and check the result...
 4.5.32: In Exercises 734, find the indefinite integral and check the result...
 4.5.33: In Exercises 734, find the indefinite integral and check the result...
 4.5.34: In Exercises 734, find the indefinite integral and check the result...
 4.5.35: In Exercises 3538, solve the differential equation. 4yx
 4.5.36: In Exercises 3538, solve the differential equation. 4yx3
 4.5.37: In Exercises 3538, solve the differential equation. yx3
 4.5.38: In Exercises 3538, solve the differential equation. x3x
 4.5.39: Slope Fields In Exercises 3942, a differential equation, a point, a...
 4.5.40: Slope Fields In Exercises 3942, a differential equation, a point, a...
 4.5.41: Slope Fields In Exercises 3942, a differential equation, a point, a...
 4.5.42: Slope Fields In Exercises 3942, a differential equation, a point, a...
 4.5.43: In Exercises 4356, find the indefinite integral. y2x3
 4.5.44: In Exercises 4356, find the indefinite integral. 2x3
 4.5.45: In Exercises 4356, find the indefinite integral. x34
 4.5.46: In Exercises 4356, find the indefinite integral. x34x
 4.5.47: In Exercises 4356, find the indefinite integral. 34xy
 4.5.48: In Exercises 4356, find the indefinite integral. 4xy
 4.5.49: In Exercises 4356, find the indefinite integral. 4xyx
 4.5.50: In Exercises 4356, find the indefinite integral. xyx2
 4.5.51: In Exercises 4356, find the indefinite integral. yx2
 4.5.52: In Exercises 4356, find the indefinite integral. x2x
 4.5.53: In Exercises 4356, find the indefinite integral. x2xy
 4.5.54: In Exercises 4356, find the indefinite integral. 2xy
 4.5.55: In Exercises 4356, find the indefinite integral. xyx
 4.5.56: In Exercises 4356, find the indefinite integral. xyx2
 4.5.57: In Exercises 5762, find an equation for the function that has the g...
 4.5.58: In Exercises 5762, find an equation for the function that has the g...
 4.5.59: In Exercises 5762, find an equation for the function that has the g...
 4.5.60: In Exercises 5762, find an equation for the function that has the g...
 4.5.61: In Exercises 5762, find an equation for the function that has the g...
 4.5.62: In Exercises 5762, find an equation for the function that has the g...
 4.5.63: In Exercises 6370, find the indefinite integral by the method shown...
 4.5.64: In Exercises 6370, find the indefinite integral by the method shown...
 4.5.65: In Exercises 6370, find the indefinite integral by the method shown...
 4.5.66: In Exercises 6370, find the indefinite integral by the method shown...
 4.5.67: In Exercises 6370, find the indefinite integral by the method shown...
 4.5.68: In Exercises 6370, find the indefinite integral by the method shown...
 4.5.69: In Exercises 6370, find the indefinite integral by the method shown...
 4.5.70: In Exercises 6370, find the indefinite integral by the method shown...
 4.5.71: In Exercises 7182, evaluate the definite integral. Use a graphing u...
 4.5.72: In Exercises 7182, evaluate the definite integral. Use a graphing u...
 4.5.73: In Exercises 7182, evaluate the definite integral. Use a graphing u...
 4.5.74: In Exercises 7182, evaluate the definite integral. Use a graphing u...
 4.5.75: In Exercises 7182, evaluate the definite integral. Use a graphing u...
 4.5.76: In Exercises 7182, evaluate the definite integral. Use a graphing u...
 4.5.77: In Exercises 7182, evaluate the definite integral. Use a graphing u...
 4.5.78: In Exercises 7182, evaluate the definite integral. Use a graphing u...
 4.5.79: In Exercises 7182, evaluate the definite integral. Use a graphing u...
 4.5.80: In Exercises 7182, evaluate the definite integral. Use a graphing u...
 4.5.81: In Exercises 7182, evaluate the definite integral. Use a graphing u...
 4.5.82: In Exercises 7182, evaluate the definite integral. Use a graphing u...
 4.5.83: Differential Equations In Exercises 8386, the graph of a function i...
 4.5.84: Differential Equations In Exercises 8386, the graph of a function i...
 4.5.85: Differential Equations In Exercises 8386, the graph of a function i...
 4.5.86: Differential Equations In Exercises 8386, the graph of a function i...
 4.5.87: In Exercises 8792, find the area of the region. Use a graphing util...
 4.5.88: In Exercises 8792, find the area of the region. Use a graphing util...
 4.5.89: In Exercises 8792, find the area of the region. Use a graphing util...
 4.5.90: In Exercises 8792, find the area of the region. Use a graphing util...
 4.5.91: In Exercises 8792, find the area of the region. Use a graphing util...
 4.5.92: In Exercises 8792, find the area of the region. Use a graphing util...
 4.5.93: In Exercises 9398, use a graphing utility to evaluate the integral....
 4.5.94: In Exercises 9398, use a graphing utility to evaluate the integral....
 4.5.95: In Exercises 9398, use a graphing utility to evaluate the integral....
 4.5.96: In Exercises 9398, use a graphing utility to evaluate the integral....
 4.5.97: In Exercises 9398, use a graphing utility to evaluate the integral....
 4.5.98: In Exercises 9398, use a graphing utility to evaluate the integral....
 4.5.99: Writing In Exercises 99 and 100, find the indefinite integral in tw...
 4.5.100: Writing In Exercises 99 and 100, find the indefinite integral in tw...
 4.5.101: In Exercises 101104, evaluate the integral using the properties of ...
 4.5.102: In Exercises 101104, evaluate the integral using the properties of ...
 4.5.103: In Exercises 101104, evaluate the integral using the properties of ...
 4.5.104: In Exercises 101104, evaluate the integral using the properties of ...
 4.5.105: Use to evaluate each definite integral without using the Fundamenta...
 4.5.106: Use the symmetry of the graphs of the sine and cosine functions as ...
 4.5.107: In Exercises 107 and 108, write the integral as the sum of the inte...
 4.5.108: In Exercises 107 and 108, write the integral as the sum of the inte...
 4.5.109: Describe why where y1x
 4.5.110: Without integrating, explain why 1x2
 4.5.111: Cash Flow The rate of disbursement of a 2 million dollar federal gr...
 4.5.112: Depreciation The rate of depreciation of a machine is inversely pro...
 4.5.113: Rainfall The normal monthly rainfall at the SeattleTacoma airport ...
 4.5.114: Sales The sales (in thousands of units) of a seasonal product are g...
 4.5.115: Water Supply A model for the flow rate of water at a pumping statio...
 4.5.116: Electricity The oscillating current in an electrical circuit is whe...
 4.5.117: Probability In Exercises 117 and 118, the function where and is a c...
 4.5.118: Probability In Exercises 117 and 118, the function where and is a c...
 4.5.119: Temperature The temperature in degrees Fahrenheit in a house is whe...
 4.5.120: Manufacturing A manufacturer of fertilizer finds that national sale...
 4.5.121: Graphical Analysis Consider the functions and where and (a) Use a g...
 4.5.122: Find by evaluating an appropriate definite integral over the interv...
 4.5.123: (a) Show that (b) Show that 12x
 4.5.124: (a) Show that (b) Show that where is a positive integer 12x4
 4.5.125: True or False? In Exercises 125130, determine whether the statement...
 4.5.126: True or False? In Exercises 125130, determine whether the statement...
 4.5.127: True or False? In Exercises 125130, determine whether the statement...
 4.5.128: True or False? In Exercises 125130, determine whether the statement...
 4.5.129: True or False? In Exercises 125130, determine whether the statement...
 4.5.130: True or False? In Exercises 125130, determine whether the statement...
 4.5.131: Assume that is continuous everywhere and that is a constant. Show t...
 4.5.132: (a) Verify that (b) Use part (a) to show that 12x2
 4.5.133: Complete the proof of Theorem 4.15. 2x2y
 4.5.134: Show that if is continuous on the entire real number line, then x2y
 4.5.135: If . . ., are real numbers satisfying show that the equation has at...
 4.5.136: Find all the continuous positive functions for such that where is a...
Solutions for Chapter 4.5: Integration by Substitution
Full solutions for Calculus  8th Edition
ISBN: 9780618502981
Solutions for Chapter 4.5: Integration by Substitution
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Calculus, edition: 8. Since 136 problems in chapter 4.5: Integration by Substitution have been answered, more than 84433 students have viewed full stepbystep solutions from this chapter. Chapter 4.5: Integration by Substitution includes 136 full stepbystep solutions. Calculus was written by and is associated to the ISBN: 9780618502981.

Addition principle of probability.
P(A or B) = P(A) + P(B)  P(A and B). If A and B are mutually exclusive events, then P(A or B) = P(A) + P(B)

Axis of symmetry
See Line of symmetry.

Coefficient matrix
A matrix whose elements are the coefficients in a system of linear equations

Component form of a vector
If a vectorâ€™s representative in standard position has a terminal point (a,b) (or (a, b, c)) , then (a,b) (or (a, b, c)) is the component form of the vector, and a and b are the horizontal and vertical components of the vector (or a, b, and c are the x, y, and zcomponents of the vector, respectively)

Data
Facts collected for statistical purposes (singular form is datum)

Directrix of a parabola, ellipse, or hyperbola
A line used to determine the conic

Ellipse
The set of all points in the plane such that the sum of the distances from a pair of fixed points (the foci) is a constant

Fibonacci sequence
The sequence 1, 1, 2, 3, 5, 8, 13, . . ..

Inferential statistics
Using the science of statistics to make inferences about the parameters in a population from a sample.

Linear combination of vectors u and v
An expression au + bv , where a and b are real numbers

Natural logarithmic function
The inverse of the exponential function y = ex, denoted by y = ln x.

Opposite
See Additive inverse of a real number and Additive inverse of a complex number.

Polar coordinate system
A coordinate system whose ordered pair is based on the directed distance from a central point (the pole) and the angle measured from a ray from the pole (the polar axis)

Projectile motion
The movement of an object that is subject only to the force of gravity

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).

Reexpression of data
A transformation of a data set.

Semiperimeter of a triangle
Onehalf of the sum of the lengths of the sides of a triangle.

Series
A finite or infinite sum of terms.

Standard form of a polar equation of a conic
r = ke 1 e cos ? or r = ke 1 e sin ? ,

Unit vector in the direction of a vector
A unit vector that has the same direction as the given vector.