 7.2.1: Use integration by parts to express  x2exdx in terms of (a) , x3 e...
 7.2.2: Write arctan x = 1 arctan x to find  arctan x dx.
 7.2.3: Find the integrals in Exercises 332.
 7.2.4: Find the integrals in Exercises 332.
 7.2.5: Find the integrals in Exercises 332.
 7.2.6: Find the integrals in Exercises 332.
 7.2.7: Find the integrals in Exercises 332.
 7.2.8: Find the integrals in Exercises 332.
 7.2.9: Find the integrals in Exercises 332.
 7.2.10: Find the integrals in Exercises 332.
 7.2.11: Find the integrals in Exercises 332.
 7.2.12: Find the integrals in Exercises 332.
 7.2.13: Find the integrals in Exercises 332.
 7.2.14: Find the integrals in Exercises 332.
 7.2.15: Find the integrals in Exercises 332.
 7.2.16: Find the integrals in Exercises 332.
 7.2.17: Find the integrals in Exercises 332.
 7.2.18: Find the integrals in Exercises 332.
 7.2.19: Find the integrals in Exercises 332.
 7.2.20: Find the integrals in Exercises 332.
 7.2.21: Find the integrals in Exercises 332.
 7.2.22: Find the integrals in Exercises 332.
 7.2.23: Find the integrals in Exercises 332.
 7.2.24: Find the integrals in Exercises 332.
 7.2.25: Find the integrals in Exercises 332.
 7.2.26: Find the integrals in Exercises 332.
 7.2.27: Find the integrals in Exercises 332.
 7.2.28: Find the integrals in Exercises 332.
 7.2.29: Find the integrals in Exercises 332.
 7.2.30: Find the integrals in Exercises 332.
 7.2.31: Find the integrals in Exercises 332.
 7.2.32: Find the integrals in Exercises 332.
 7.2.33: Evaluate the integrals in Exercises 3340 both exactly [e.g. ln(3)] ...
 7.2.34: Evaluate the integrals in Exercises 3340 both exactly [e.g. ln(3)] ...
 7.2.35: Evaluate the integrals in Exercises 3340 both exactly [e.g. ln(3)] ...
 7.2.36: Evaluate the integrals in Exercises 3340 both exactly [e.g. ln(3)] ...
 7.2.37: Evaluate the integrals in Exercises 3340 both exactly [e.g. ln(3)] ...
 7.2.38: Evaluate the integrals in Exercises 3340 both exactly [e.g. ln(3)] ...
 7.2.39: Evaluate the integrals in Exercises 3340 both exactly [e.g. ln(3)] ...
 7.2.40: Evaluate the integrals in Exercises 3340 both exactly [e.g. ln(3)] ...
 7.2.41: For each of the following integrals, indicate whether integration b...
 7.2.42: Find  2 1 ln x dx numerically. Find  2 1 ln x dx using antideriva...
 7.2.43: In 4345, using properties of ln, find a substitution w and constant...
 7.2.44: In 4345, using properties of ln, find a substitution w and constant...
 7.2.45: In 4345, using properties of ln, find a substitution w and constant...
 7.2.46: In 4651, find the exact area.
 7.2.47: In 4651, find the exact area.
 7.2.48: In 4651, find the exact area.
 7.2.49: In 4651, find the exact area.
 7.2.50: In 4651, find the exact area.
 7.2.51: In 4651, find the exact area.
 7.2.52: In Exercise 13, you evaluated  sin2 d using integration by parts. ...
 7.2.53: Compute  cos2 d in two different ways and explain any differences ...
 7.2.54: Use integration by parts twice to find  ex sin x dx.
 7.2.55: Use integration by parts twice to find  e cos d.
 7.2.56: Use the results from 54 and 55 and integration by parts to find  x...
 7.2.57: Use the results from 54 and 55 and integration by parts to find  e...
 7.2.58: If f is a twice differentiable function, find , f (x) ln x dx + , f...
 7.2.59: . If f is a twice differentiable function, find  xf(x) dx. (Your a...
 7.2.60: Use the table with f(x) = F (x) to find , 5 0 xf (x) dx.
 7.2.61: In 6164, derive the given formulas.
 7.2.62: In 6164, derive the given formulas.
 7.2.63: In 6164, derive the given formulas.
 7.2.64: In 6164, derive the given formulas.
 7.2.65: In 6164, derive the given formulas.
 7.2.66: Estimate  10 0 f(x)g (x) dx if f(x) = x2 and g has the values in t...
 7.2.67: Let f be a function with f(0) = 6, f(1) = 5, and f (1) = 2. Evaluat...
 7.2.68: Given h(x) = f(x) x and g (x) = f(x)/ x, rewrite in terms of h(x) a...
 7.2.69: Given that f(7) = 0 and  7 0 f(x) dx = 5, evaluate , 7 0 xf (x) dx.
 7.2.70: Let F(a) be the area under the graph of y = x2ex between x = 0 and ...
 7.2.71: The concentration, C, in ng/ml, of a drug in the blood as a functio...
 7.2.72: The voltage, V , in an electric circuit is given as a function of t...
 7.2.73: During a surge in the demand for electricity, the rate, r, at which...
 7.2.74: Given h(x) = f(x) ln x and g (x) = f(x) x , rewrite , f (x) ln x...
 7.2.75: The error function, erf(x), is defined by erf(x) = 2 , x 0 et2 dt. ...
 7.2.76: The Eulerian logarithmic integral Li(x) is defined2 as Li(x) = , x ...
 7.2.77: To integrate  tln t dt by parts, use u = t, v = ln t.
 7.2.78: The integral  arctan x dx cannot be evaluated using integration by...
 7.2.79: Using integration by parts, we can show that , f(x) dx = xf (x) , x...
 7.2.80: An integral using only powers of and sin which can be evaluated usi...
 7.2.81: An integral that requires three applications of integration by part
 7.2.82: An integral of the form  f(x)g(x) dx that can be evaluated using i...
 7.2.83: In 8385, decide whether the statements are true or false. Give an e...
 7.2.84: In 8385, decide whether the statements are true or false. Give an e...
 7.2.85: In 8385, decide whether the statements are true or false. Give an e...
Solutions for Chapter 7.2: INTEGRATION BY PARTS
Full solutions for Calculus: Single Variable  6th Edition
ISBN: 9780470888643
Solutions for Chapter 7.2: INTEGRATION BY PARTS
Get Full SolutionsChapter 7.2: INTEGRATION BY PARTS includes 85 full stepbystep solutions. This textbook survival guide was created for the textbook: Calculus: Single Variable , edition: 6. Calculus: Single Variable was written by and is associated to the ISBN: 9780470888643. This expansive textbook survival guide covers the following chapters and their solutions. Since 85 problems in chapter 7.2: INTEGRATION BY PARTS have been answered, more than 33165 students have viewed full stepbystep solutions from this chapter.

Confounding variable
A third variable that affects either of two variables being studied, making inferences about causation unreliable

Convergence of a series
A series aqk=1 ak converges to a sum S if imn: q ank=1ak = S

Directed distance
See Polar coordinates.

Discriminant
For the equation ax 2 + bx + c, the expression b2  4ac; for the equation Ax2 + Bxy + Cy2 + Dx + Ey + F = 0, the expression B2  4AC

Equal complex numbers
Complex numbers whose real parts are equal and whose imaginary parts are equal.

Imaginary part of a complex number
See Complex number.

Lefthand limit of f at x a
The limit of ƒ as x approaches a from the left.

Linear regression line
The line for which the sum of the squares of the residuals is the smallest possible

Mathematical induction
A process for proving that a statement is true for all natural numbers n by showing that it is true for n = 1 (the anchor) and that, if it is true for n = k, then it must be true for n = k + 1 (the inductive step)

Measure of spread
A measure that tells how widely distributed data are.

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

Normal distribution
A distribution of data shaped like the normal curve.

nth root
See Principal nth root

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

Principal nth root
If bn = a, then b is an nth root of a. If bn = a and a and b have the same sign, b is the principal nth root of a (see Radical), p. 508.

Principle of mathematical induction
A principle related to mathematical induction.

Proportional
See Power function

Random behavior
Behavior that is determined only by the laws of probability.

Sum of an infinite geometric series
Sn = a 1  r , r 6 1

Synthetic division
A procedure used to divide a polynomial by a linear factor, x  a