 7.2.1: Use integration by parts to express  x2exdx in terms of(a),x3exdx ...
 7.2.2: Write arctan x = 1 arctan x to find  arctan x dx.
 7.2.3: Find the integrals in Exercises 332.,t sin t dt
 7.2.4: Find the integrals in Exercises 332.,t2 sin t dt
 7.2.5: Find the integrals in Exercises 332.,te5t dt
 7.2.6: Find the integrals in Exercises 332.,t2e5t dt
 7.2.7: Find the integrals in Exercises 332.,pe0.1p dp
 7.2.8: Find the integrals in Exercises 332.,(z + 1)e2z dz
 7.2.9: Find the integrals in Exercises 332.,x ln x dx
 7.2.10: Find the integrals in Exercises 332.,x3 ln x dx
 7.2.11: Find the integrals in Exercises 332.,q5 ln 5q dq
 7.2.12: Find the integrals in Exercises 332.,2 cos 3 d
 7.2.13: Find the integrals in Exercises 332.,sin2 d
 7.2.14: Find the integrals in Exercises 332.,cos2(3 + 1) d
 7.2.15: Find the integrals in Exercises 332.,(ln t)2 dt
 7.2.16: Find the integrals in Exercises 332.,ln(x2) dx
 7.2.17: Find the integrals in Exercises 332.,yy + 3 dy
 7.2.18: Find the integrals in Exercises 332.,(t + 2)2+3t dt
 7.2.19: Find the integrals in Exercises 332.,( + 1) sin( + 1) d 2
 7.2.20: Find the integrals in Exercises 332., zez dz
 7.2.21: Find the integrals in Exercises 332., ln xx2 dx
 7.2.22: Find the integrals in Exercises 332., y5 ydy
 7.2.23: Find the integrals in Exercises 332., t + 75 tdt
 7.2.24: Find the integrals in Exercises 332.,x(ln x)4 dx
 7.2.25: Find the integrals in Exercises 332.,r(ln r)2 dr
 7.2.26: Find the integrals in Exercises 332.,arcsin w dw
 7.2.27: Find the integrals in Exercises 332.,arctan 7z dz
 7.2.28: Find the integrals in Exercises 332.,x arctan x2 dx
 7.2.29: Find the integrals in Exercises 332.,x3ex2dx
 7.2.30: Find the integrals in Exercises 332.,x5 cos x3 dx
 7.2.31: Find the integrals in Exercises 332.,x sinh x dx
 7.2.32: Find the integrals in Exercises 332.,(x 1) cosh x dx
 7.2.33: Evaluate the integrals in Exercises 3340 both exactly [e.g.ln(3)] a...
 7.2.34: Evaluate the integrals in Exercises 3340 both exactly [e.g.ln(3)] a...
 7.2.35: Evaluate the integrals in Exercises 3340 both exactly [e.g.ln(3)] a...
 7.2.36: Evaluate the integrals in Exercises 3340 both exactly [e.g.ln(3)] a...
 7.2.37: Evaluate the integrals in Exercises 3340 both exactly [e.g.ln(3)] a...
 7.2.38: Evaluate the integrals in Exercises 3340 both exactly [e.g.ln(3)] a...
 7.2.39: Evaluate the integrals in Exercises 3340 both exactly [e.g.ln(3)] a...
 7.2.40: Evaluate the integrals in Exercises 3340 both exactly [e.g.ln(3)] a...
 7.2.41: For each of the following integrals, indicate whether integrationby...
 7.2.42: Find  21 ln x dx numerically. Find  21 ln x dx using antiderivati...
 7.2.43: In 4345, using properties of ln, find a substitutionw and constant ...
 7.2.44: In 4345, using properties of ln, find a substitutionw and constant ...
 7.2.45: In 4345, using properties of ln, find a substitutionw and constant ...
 7.2.46: In 4651, find the exact area.Under y = tet for 0 t 2.
 7.2.47: In 4651, find the exact area.Under f(z) = arctan z for 0 z 2.
 7.2.48: In 4651, find the exact area.Under f(y) = arcsin y for 0 y 1.
 7.2.49: In 4651, find the exact area.Between y = ln x and y = ln(x2) for 1 ...
 7.2.50: In 4651, find the exact area.Between f(t) = ln(t2 1) and g(t) = ln(...
 7.2.51: In 4651, find the exact area.Under the first arch of f(x) = x sin x.
 7.2.52: In Exercise 13, you evaluated  sin2 d using integrationby parts. (...
 7.2.53: Compute  cos2 d in two different ways and explainany differences i...
 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 integrationby parts to find  xe...
 7.2.57: Use the results from 54 and 55 and integrationby parts to find  e ...
 7.2.58: If f is a twice differentiable function, find,f(x) ln x dx +, f(x)x...
 7.2.59: If f is a twice differentiable function, find  xf(x) dx.(Your answ...
 7.2.60: Use the table with f(x) = F(x) to find , 50xf(x) dx.
 7.2.61: In 6164, derive the given formulas.,xnex dx = xnex n,xn1ex dx
 7.2.62: In 6164, derive the given formulas.,xn cos ax dx = 1axn sin ax na,x...
 7.2.63: In 6164, derive the given formulas.,xn sin ax dx = 1axn cos ax+na,x...
 7.2.64: In 6164, derive the given formulas.,cosn x dx = 1n cosn1 x sin x+n ...
 7.2.65: Integrating eax sin bx by parts twice gives,eax sin bx dx = eax(A s...
 7.2.66: Estimate  100 f(x)g(x) dx if f(x) = x2 and g has thevalues in the ...
 7.2.67: Let f be a function with f(0) = 6, f(1) = 5, andf(1) = 2. Evaluate ...
 7.2.68: Given h(x) = f(x)x and g(x) = f(x)/x, rewritein terms of h(x) and g...
 7.2.69: Given that f(7) = 0 and  70 f(x) dx = 5, evaluate, 70xf(x) dx.
 7.2.70: Let F(a) be the area under the graph of y = x2ex betweenx = 0 and x...
 7.2.71: The concentration, C, in ng/ml, of a drug in the bloodas a function...
 7.2.72: The voltage, V , in an electric circuit is given as a functionof ti...
 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 dx....
 7.2.75: The error function, erf(x), is defined byerf(x) = 2, x0et2dt.(a) Le...
 7.2.76: The Eulerian logarithmic integral Li(x) is defined2 asLi(x) = , x21...
 7.2.77: In 7779, explain what is wrong with the statement.To integrate  tl...
 7.2.78: In 7779, explain what is wrong with the statement.The integral  ar...
 7.2.79: In 7779, explain what is wrong with the statement.Using integration...
 7.2.80: In 8082, give an example of:An integral using only powers of and si...
 7.2.81: In 8082, give an example of:An integral that requires three applica...
 7.2.82: In 8082, give an example of:An integral of the form  f(x)g(x) dx t...
 7.2.83: In 8385, decide whether the statements are true orfalse. Give an ex...
 7.2.84: In 8385, decide whether the statements are true orfalse. Give an ex...
 7.2.85: In 8385, decide whether the statements are true orfalse. Give an ex...
Solutions for Chapter 7.2: INTEGRATION BY PARTS
Full solutions for Calculus: Single and Multivariable  6th Edition
ISBN: 9780470888612
Solutions for Chapter 7.2: INTEGRATION BY PARTS
Get Full SolutionsThis textbook survival guide was created for the textbook: Calculus: Single and Multivariable , edition: 6. Calculus: Single and Multivariable was written by and is associated to the ISBN: 9780470888612. 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 42444 students have viewed full stepbystep solutions from this chapter. Chapter 7.2: INTEGRATION BY PARTS includes 85 full stepbystep solutions.

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)

Bounded below
A function is bounded below if there is a number b such that b ? ƒ(x) for all x in the domain of f.

Common ratio
See Geometric sequence.

Cone
See Right circular cone.

Focal axis
The line through the focus and perpendicular to the directrix of a conic.

Integers
The numbers . . ., 3, 2, 1, 0,1,2,...2

Leading term
See Polynomial function in x.

Negative association
A relationship between two variables in which higher values of one variable are generally associated with lower values of the other variable.

Plane in Cartesian space
The graph of Ax + By + Cz + D = 0, where A, B, and C are not all zero.

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

Power function
A function of the form ƒ(x) = k . x a, where k and a are nonzero constants. k is the constant of variation and a is the power.

Probability of an event in a finite sample space of equally likely outcomes
The number of outcomes in the event divided by the number of outcomes in the sample space.

Randomization
The principle of experimental design that makes it possible to use the laws of probability when making inferences.

Response variable
A variable that is affected by an explanatory variable.

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

Solve algebraically
Use an algebraic method, including paper and pencil manipulation and obvious mental work, with no calculator or grapher use. When appropriate, the final exact solution may be approximated by a calculator

Sum of a finite geometric series
Sn = a111  r n 2 1  r

Symmetric about the origin
A graph in which (x, y) is on the the graph whenever (x, y) is; or a graph in which (r, ?) or (r, ? + ?) is on the graph whenever (r, ?) is

Terminal point
See Arrow.

yintercept
A point that lies on both the graph and the yaxis.