 8.2.1: In Exercises 16, identify and for finding the integral using integr...
 8.2.2: In Exercises 16, identify and for finding the integral using integr...
 8.2.3: In Exercises 16, identify and for finding the integral using integr...
 8.2.4: In Exercises 16, identify and for finding the integral using integr...
 8.2.5: In Exercises 16, identify and for finding the integral using integr...
 8.2.6: In Exercises 16, identify and for finding the integral using integr...
 8.2.7: x3 ln x dx; u ln x, dv x3 dx
 8.2.8: 4x 7)ex dx; u 4x 7, dv ex dx
 8.2.9: x sin 3x dx; u x, dv sin 3x dx
 8.2.10: x cos 4x dx; u x, dv cos 4x dx
 8.2.11: In Exercises 1138, find the integral. (Note: Solve by the simplest ...
 8.2.12: In Exercises 1138, find the integral. (Note: Solve by the simplest ...
 8.2.13: In Exercises 1138, find the integral. (Note: Solve by the simplest ...
 8.2.14: In Exercises 1138, find the integral. (Note: Solve by the simplest ...
 8.2.15: In Exercises 1138, find the integral. (Note: Solve by the simplest ...
 8.2.16: In Exercises 1138, find the integral. (Note: Solve by the simplest ...
 8.2.17: In Exercises 1138, find the integral. (Note: Solve by the simplest ...
 8.2.18: In Exercises 1138, find the integral. (Note: Solve by the simplest ...
 8.2.19: In Exercises 1138, find the integral. (Note: Solve by the simplest ...
 8.2.20: In Exercises 1138, find the integral. (Note: Solve by the simplest ...
 8.2.21: In Exercises 1138, find the integral. (Note: Solve by the simplest ...
 8.2.22: In Exercises 1138, find the integral. (Note: Solve by the simplest ...
 8.2.23: In Exercises 1138, find the integral. (Note: Solve by the simplest ...
 8.2.24: In Exercises 1138, find the integral. (Note: Solve by the simplest ...
 8.2.25: In Exercises 1138, find the integral. (Note: Solve by the simplest ...
 8.2.26: In Exercises 1138, find the integral. (Note: Solve by the simplest ...
 8.2.27: In Exercises 1138, find the integral. (Note: Solve by the simplest ...
 8.2.28: In Exercises 1138, find the integral. (Note: Solve by the simplest ...
 8.2.29: In Exercises 1138, find the integral. (Note: Solve by the simplest ...
 8.2.30: In Exercises 1138, find the integral. (Note: Solve by the simplest ...
 8.2.31: In Exercises 1138, find the integral. (Note: Solve by the simplest ...
 8.2.32: In Exercises 1138, find the integral. (Note: Solve by the simplest ...
 8.2.33: In Exercises 1138, find the integral. (Note: Solve by the simplest ...
 8.2.34: In Exercises 1138, find the integral. (Note: Solve by the simplest ...
 8.2.35: In Exercises 1138, find the integral. (Note: Solve by the simplest ...
 8.2.36: In Exercises 1138, find the integral. (Note: Solve by the simplest ...
 8.2.37: In Exercises 1138, find the integral. (Note: Solve by the simplest ...
 8.2.38: In Exercises 1138, find the integral. (Note: Solve by the simplest ...
 8.2.39: In Exercises 39 44, solve the differential equation.
 8.2.40: In Exercises 39 44, solve the differential equation.
 8.2.41: In Exercises 39 44, solve the differential equation.
 8.2.42: In Exercises 39 44, solve the differential equation.
 8.2.43: In Exercises 39 44, solve the differential equation.
 8.2.44: In Exercises 39 44, solve the differential equation.
 8.2.45: In Exercises 45 and 46, a differential equation, a point, and a slo...
 8.2.46: In Exercises 45 and 46, a differential equation, a point, and a slo...
 8.2.47: In Exercises 47 and 48, use a computer algebra system to graph the ...
 8.2.48: In Exercises 47 and 48, use a computer algebra system to graph the ...
 8.2.49: In Exercises 4960, evaluate the definite integral. Use a graphing u...
 8.2.50: In Exercises 4960, evaluate the definite integral. Use a graphing u...
 8.2.51: In Exercises 4960, evaluate the definite integral. Use a graphing u...
 8.2.52: In Exercises 4960, evaluate the definite integral. Use a graphing u...
 8.2.53: In Exercises 4960, evaluate the definite integral. Use a graphing u...
 8.2.54: In Exercises 4960, evaluate the definite integral. Use a graphing u...
 8.2.55: In Exercises 4960, evaluate the definite integral. Use a graphing u...
 8.2.56: In Exercises 4960, evaluate the definite integral. Use a graphing u...
 8.2.57: In Exercises 4960, evaluate the definite integral. Use a graphing u...
 8.2.58: In Exercises 4960, evaluate the definite integral. Use a graphing u...
 8.2.59: In Exercises 4960, evaluate the definite integral. Use a graphing u...
 8.2.60: In Exercises 4960, evaluate the definite integral. Use a graphing u...
 8.2.61: In Exercises 61 66, use the tabular method to find the integral.
 8.2.62: In Exercises 61 66, use the tabular method to find the integral.
 8.2.63: In Exercises 61 66, use the tabular method to find the integral.
 8.2.64: In Exercises 61 66, use the tabular method to find the integral.
 8.2.65: In Exercises 61 66, use the tabular method to find the integral.
 8.2.66: In Exercises 61 66, use the tabular method to find the integral.
 8.2.67: In Exercises 6774, find or evaluate the integral using substitution...
 8.2.68: In Exercises 6774, find or evaluate the integral using substitution...
 8.2.69: In Exercises 6774, find or evaluate the integral using substitution...
 8.2.70: In Exercises 6774, find or evaluate the integral using substitution...
 8.2.71: In Exercises 6774, find or evaluate the integral using substitution...
 8.2.72: In Exercises 6774, find or evaluate the integral using substitution...
 8.2.73: In Exercises 6774, find or evaluate the integral using substitution...
 8.2.74: In Exercises 6774, find or evaluate the integral using substitution...
 8.2.75: Integration by parts is based on what differentiation rule? Explain.
 8.2.76: In your own words, state how you determine which parts of the integ...
 8.2.77: When evaluating explain how letting and makes the solution more dif...
 8.2.78: State whether you would use integration by parts to evaluate each i...
 8.2.79: In Exercises 79 82, use a computer algebra system to (a) find or ev...
 8.2.80: In Exercises 79 82, use a computer algebra system to (a) find or ev...
 8.2.81: In Exercises 79 82, use a computer algebra system to (a) find or ev...
 8.2.82: In Exercises 79 82, use a computer algebra system to (a) find or ev...
 8.2.83: Integrate (a) by parts, letting (b) by substitution, letting
 8.2.84: Integrate (a) by parts, letting (b) by substitution, letting
 8.2.85: Integrate (a) by parts, letting (b) by substitution, letting
 8.2.86: Integrate (a) by parts, letting (b) by substitution, letting
 8.2.87: In Exercises 87 and 88, use a computer algebra system to find the i...
 8.2.88: In Exercises 87 and 88, use a computer algebra system to find the i...
 8.2.89: x n sin x dx x n cos x n x n1 cos x dx
 8.2.90: x n cos x dx x n sin x n x n1 sin x dx
 8.2.91: x n ln x dx x n1 n 12 1 n 1 ln x C
 8.2.92: x n eax dx x n eax a n a x n1 eax dx
 8.2.93: eax sin bx dx eaxa sin bx b cos bx a2 b2 C
 8.2.94: eax cos bx dx eaxa cos bx b sin bx a2 b2 C
 8.2.95: In Exercises 9598, find the integral by using the appropriate formu...
 8.2.96: In Exercises 9598, find the integral by using the appropriate formu...
 8.2.97: In Exercises 9598, find the integral by using the appropriate formu...
 8.2.98: In Exercises 9598, find the integral by using the appropriate formu...
 8.2.99: y 2xex , y 0, x 3
 8.2.100: y 1 16 xex 4 , y 0, x 0, x 4
 8.2.101: y ex sin x, y 0, x 1
 8.2.102: y x sin x, y 0, x
 8.2.103: Given the region bounded by the graphs of and find (a) the area of ...
 8.2.104: Given the region bounded by the graphs of and find (a) the volume o...
 8.2.105: Find the centroid of the region bounded by the graphs of and How is...
 8.2.106: Find the centroid of the region bounded by the graphs of and x=4
 8.2.107: A damping force affects the vibration of a spring so that the displ...
 8.2.108: A model for the ability of a child to memorize, measured on a scale...
 8.2.109: ct 100,000 4000t, r 5%, t1 10
 8.2.110: ct 30,000 500t, r 7%, t1 5
 8.2.111: x sin nx dx 2 n 2 n , , n is odd n is even
 8.2.112: x2 cos nx dx 1n 4 n2
 8.2.113: A string stretched between the two points and is plucked by displac...
 8.2.114: Find the fallacy in the following argument that 0 dx x 1 x x 1 x2 x...
 8.2.115: Let be positive and strictly increasing on the interval Consider th...
 8.2.116: Consider the differential equation with the initial condition (a) U...
 8.2.117: In Exercises 117 and 118, consider the differential equation and re...
 8.2.118: In Exercises 117 and 118, consider the differential equation and re...
 8.2.119: Give a geometric explanation of why Verify the inequality by evalua...
 8.2.120: Find the area bounded by the graphs of and over each interval. (a) ...
Solutions for Chapter 8.2: Integration by Parts
Full solutions for Calculus  9th Edition
ISBN: 9780547167022
Solutions for Chapter 8.2: Integration by Parts
Get Full SolutionsThis textbook survival guide was created for the textbook: Calculus , edition: 9. Calculus was written by and is associated to the ISBN: 9780547167022. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 8.2: Integration by Parts includes 120 full stepbystep solutions. Since 120 problems in chapter 8.2: Integration by Parts have been answered, more than 63891 students have viewed full stepbystep solutions from this chapter.

Addition property of equality
If u = v and w = z , then u + w = v + z

Ambiguous case
The case in which two sides and a nonincluded angle can determine two different triangles

Aphelion
The farthest point from the Sun in a planet’s orbit

artesian coordinate system
An association between the points in a plane and ordered pairs of real numbers; or an association between the points in threedimensional space and ordered triples of real numbers

Compound interest
Interest that becomes part of the investment

Definite integral
The definite integral of the function ƒ over [a,b] is Lbaƒ(x) dx = limn: q ani=1 ƒ(xi) ¢x provided the limit of the Riemann sums exists

Descriptive statistics
The gathering and processing of numerical information

Fitting a line or curve to data
Finding a line or curve that comes close to passing through all the points in a scatter plot.

Increasing on an interval
A function ƒ is increasing on an interval I if, for any two points in I, a positive change in x results in a positive change in.

Measure of an angle
The number of degrees or radians in an angle

Multiplicative inverse of a real number
The reciprocal of b, or 1/b, b Z 0

Natural numbers
The numbers 1, 2, 3, . . . ,.

NDER ƒ(a)
See Numerical derivative of ƒ at x = a.

Numerical derivative of ƒ at a
NDER f(a) = ƒ1a + 0.0012  ƒ1a  0.00120.002

Open interval
An interval that does not include its endpoints.

Product of matrices A and B
The matrix in which each entry is obtained by multiplying the entries of a row of A by the corresponding entries of a column of B and then adding

Secant
The function y = sec x.

Sum of two vectors
<u1, u2> + <v1, v2> = <u1 + v1, u2 + v2> <u1 + v1, u2 + v2, u3 + v3>

Velocity
A vector that specifies the motion of an object in terms of its speed and direction.

Vertices of a hyperbola
The points where a hyperbola intersects the line containing its foci.