 7.1.1: 12 Evaluate the integral using integration by parts with the indica...
 7.1.2: 12 Evaluate the integral using integration by parts with the indica...
 7.1.3: 336 Evaluate the integral
 7.1.4: 336 Evaluate the integral
 7.1.5: 336 Evaluate the integral
 7.1.6: 336 Evaluate the integral
 7.1.7: 336 Evaluate the integral
 7.1.8: 336 Evaluate the integral
 7.1.9: 336 Evaluate the integral
 7.1.10: 336 Evaluate the integral
 7.1.11: 336 Evaluate the integral
 7.1.12: 336 Evaluate the integral
 7.1.13: 336 Evaluate the integral
 7.1.14: 336 Evaluate the integral
 7.1.15: 336 Evaluate the integral
 7.1.16: 336 Evaluate the integral
 7.1.17: 336 Evaluate the integral
 7.1.18: 336 Evaluate the integral
 7.1.19: 336 Evaluate the integral
 7.1.20: 336 Evaluate the integral
 7.1.21: 336 Evaluate the integral
 7.1.22: 336 Evaluate the integral
 7.1.23: 336 Evaluate the integral
 7.1.24: 336 Evaluate the integral
 7.1.25: 336 Evaluate the integral
 7.1.26: 336 Evaluate the integral
 7.1.27: 336 Evaluate the integral
 7.1.28: 336 Evaluate the integral
 7.1.29: 336 Evaluate the integral
 7.1.30: 336 Evaluate the integral
 7.1.31: 336 Evaluate the integral
 7.1.32: 336 Evaluate the integral
 7.1.33: 336 Evaluate the integral
 7.1.34: 336 Evaluate the integral
 7.1.35: 336 Evaluate the integral
 7.1.36: 336 Evaluate the integral
 7.1.37: 3742 First make a substitution and then use integration by parts to...
 7.1.38: 3742 First make a substitution and then use integration by parts to...
 7.1.39: 3742 First make a substitution and then use integration by parts to...
 7.1.40: 3742 First make a substitution and then use integration by parts to...
 7.1.41: 3742 First make a substitution and then use integration by parts to...
 7.1.42: 3742 First make a substitution and then use integration by parts to...
 7.1.43: 4346 Evaluate the indefinite integral. Illustrate, and check that y...
 7.1.44: 4346 Evaluate the indefinite integral. Illustrate, and check that y...
 7.1.45: 4346 Evaluate the indefinite integral. Illustrate, and check that y...
 7.1.46: 4346 Evaluate the indefinite integral. Illustrate, and check that y...
 7.1.47: (a) Use the reduction formula in Example 6 to show that y sin2 x dx...
 7.1.48: (a) Prove the reduction formula y cosn x dx 1 n cosn21 x sin x 1 n ...
 7.1.49: (a) Use the reduction formula in Example 6 to show that y y2 0 sinn...
 7.1.50: Prove that, for even powers of sine, y y2 0 sin2n x dx 1 ? 3 ? 5 ? ...
 7.1.51: 5154 Use integration by parts to prove the reduction formula.
 7.1.52: 5154 Use integration by parts to prove the reduction formula.
 7.1.53: 5154 Use integration by parts to prove the reduction formula.
 7.1.54: 5154 Use integration by parts to prove the reduction formula.
 7.1.55: Use Exercise 51 to find y sln xd 3 dx.
 7.1.56: Use Exercise 52 to find y x 4 ex dx.
 7.1.57: 5758 Find the area of the region bounded by the given curves
 7.1.58: 5758 Find the area of the region bounded by the given curves
 7.1.59: 5960 Use a graph to find approximate xcoordinates of the points of...
 7.1.60: 5960 Use a graph to find approximate xcoordinates of the points of...
 7.1.61: 6164 Use the method of cylindrical shells to find the volume genera...
 7.1.62: 6164 Use the method of cylindrical shells to find the volume genera...
 7.1.63: 6164 Use the method of cylindrical shells to find the volume genera...
 7.1.64: 6164 Use the method of cylindrical shells to find the volume genera...
 7.1.65: Calculate the volume generated by rotating the region bounded by th...
 7.1.66: Calculate the average value of fsxd x sec2 x on the interval f0, y4g
 7.1.67: The Fresnel function Ssxd y x 0 sin(1 2 t 2 ) dt was discussed in E...
 7.1.68: A rocket accelerates by burning its onboard fuel, so its mass decre...
 7.1.69: A particle that moves along a straight line has velocity vstd t 2 e...
 7.1.70: If fs0d ts0d 0 and f 0 and t 0 are continuous, show that y a 0
 7.1.71: Suppose that fs1d 2, fs4d 7, f9s1d 5, f9s4d 3, and f 0 is continuou...
 7.1.72: (a) Use integration by parts to show that y fsxd dx xfsxd 2 y xf9sx...
 7.1.73: We arrived at Formula 6.3.2, V y b a 2x fsxd dx, by using cylindric...
 7.1.74: Let In y y2 0 sinn x dx. (a) Show that I2n12 < I2n11 < I2n. (b) Use...
Solutions for Chapter 7.1: Integration by Parts
Full solutions for Single Variable Calculus: Early Transcendentals  8th Edition
ISBN: 9781305270336
Solutions for Chapter 7.1: Integration by Parts
Get Full SolutionsThis textbook survival guide was created for the textbook: Single Variable Calculus: Early Transcendentals, edition: 8. Single Variable Calculus: Early Transcendentals was written by and is associated to the ISBN: 9781305270336. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 7.1: Integration by Parts includes 74 full stepbystep solutions. Since 74 problems in chapter 7.1: Integration by Parts have been answered, more than 42129 students have viewed full stepbystep solutions from this chapter.

Arccosine function
See Inverse cosine function.

Common ratio
See Geometric sequence.

Compound fraction
A fractional expression in which the numerator or denominator may contain fractions

Correlation coefficient
A measure of the strength of the linear relationship between two variables, pp. 146, 162.

equation of an ellipse
(x  h2) a2 + (y  k)2 b2 = 1 or (y  k)2 a2 + (x  h)2 b2 = 1

Explicitly defined sequence
A sequence in which the kth term is given as a function of k.

Exponent
See nth power of a.

General form (of a line)
Ax + By + C = 0, where A and B are not both zero.

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

Instantaneous rate of change
See Derivative at x = a.

Integrable over [a, b] Lba
ƒ1x2 dx exists.

Intercepted arc
Arc of a circle between the initial side and terminal side of a central angle.

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

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

Period
See Periodic function.

Piecewisedefined function
A function whose domain is divided into several parts with a different function rule applied to each part, p. 104.

Polynomial interpolation
The process of fitting a polynomial of degree n to (n + 1) points.

Solve by elimination or substitution
Methods for solving systems of linear equations.

System
A set of equations or inequalities.

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.