 7.2.1: On which derivative rule is integration by parts based?
 7.2.2: How would you choose dv when evaluating 1xn eax dx using integratio...
 7.2.3: How would you choose u when evaluating 1xn cos ax dx using integrat...
 7.2.4: Explain how integration by parts is used to evaluate a definite int...
 7.2.5: What type of integrand is a good candidate for integration by parts?
 7.2.6: What choices for u and dv simplify 1tan1 x dx?
 7.2.7: 722. Integration by parts Evaluate the following integrals. L x cos...
 7.2.8: 722. Integration by parts Evaluate the following integrals. L x sin...
 7.2.9: 722. Integration by parts Evaluate the following integrals. L tet dt
 7.2.10: 722. Integration by parts Evaluate the following integrals. L 2xe3x dx
 7.2.11: 722. Integration by parts Evaluate the following integrals. L x 2x ...
 7.2.12: 722. Integration by parts Evaluate the following integrals. L se2s ds
 7.2.13: 722. Integration by parts Evaluate the following integrals. L x2 ln...
 7.2.14: 722. Integration by parts Evaluate the following integrals. L u sec...
 7.2.15: 722. Integration by parts Evaluate the following integrals. L x2 ln...
 7.2.16: 722. Integration by parts Evaluate the following integrals. L x ln ...
 7.2.17: 722. Integration by parts Evaluate the following integrals. L ln x ...
 7.2.18: 722. Integration by parts Evaluate the following integrals. L sin1...
 7.2.19: 722. Integration by parts Evaluate the following integrals. L tan1...
 7.2.20: 722. Integration by parts Evaluate the following integrals. L x sec...
 7.2.21: 722. Integration by parts Evaluate the following integrals. L x sin...
 7.2.22: 722. Integration by parts Evaluate the following integrals. L x tan...
 7.2.23: 2330. Repeated integration by parts Evaluate the following integral...
 7.2.24: 2330. Repeated integration by parts Evaluate the following integral...
 7.2.25: 2330. Repeated integration by parts Evaluate the following integral...
 7.2.26: 2330. Repeated integration by parts Evaluate the following integral...
 7.2.27: 2330. Repeated integration by parts Evaluate the following integral...
 7.2.28: 2330. Repeated integration by parts Evaluate the following integral...
 7.2.29: 2330. Repeated integration by parts Evaluate the following integral...
 7.2.30: 2330. Repeated integration by parts Evaluate the following integral...
 7.2.31: 3138. Definite integrals Evaluate the following definite integrals....
 7.2.32: 3138. Definite integrals Evaluate the following definite integrals....
 7.2.33: 3138. Definite integrals Evaluate the following definite integrals....
 7.2.34: 3138. Definite integrals Evaluate the following definite integrals....
 7.2.35: 3138. Definite integrals Evaluate the following definite integrals....
 7.2.36: 3138. Definite integrals Evaluate the following definite integrals....
 7.2.37: 3138. Definite integrals Evaluate the following definite integrals....
 7.2.38: 3138. Definite integrals Evaluate the following definite integrals....
 7.2.39: 3942. Volumes of solids Find the volume of the solid that is genera...
 7.2.40: 3942. Volumes of solids Find the volume of the solid that is genera...
 7.2.41: 3942. Volumes of solids Find the volume of the solid that is genera...
 7.2.42: 3942. Volumes of solids Find the volume of the solid that is genera...
 7.2.43: Explain why or why not Determine whether the following statements a...
 7.2.44: 4447. Reduction formulas Use integration by parts to derive the fol...
 7.2.45: 4447. Reduction formulas Use integration by parts to derive the fol...
 7.2.46: 4447. Reduction formulas Use integration by parts to derive the fol...
 7.2.47: 4447. Reduction formulas Use integration by parts to derive the fol...
 7.2.48: 4851. Applying reduction formulas Use the reduction formulas in Exe...
 7.2.49: 4851. Applying reduction formulas Use the reduction formulas in Exe...
 7.2.50: 4851. Applying reduction formulas Use the reduction formulas in Exe...
 7.2.51: 4851. Applying reduction formulas Use the reduction formulas in Exe...
 7.2.52: 5253. Integrals involving 1ln x dx Use a substitution to reduce the...
 7.2.53: 5253. Integrals involving 1ln x dx Use a substitution to reduce the...
 7.2.54: Two methods a. Evaluate 1x ln x2 dx using the substitution u = x2 a...
 7.2.55: Logarithm base b Prove that 1logb x dx = 1 ln b 1x ln x  x2 + C.
 7.2.56: Two integration methods Evaluate 1sin x cos x dx using integration ...
 7.2.57: Combining two integration methods Evaluate 1cos 1x dx using a subst...
 7.2.58: Combining two integration methods Evaluate 1 p 2>4 0 sin 1x dx usin...
 7.2.59: Function defined as an integral Find the arc length of the function...
 7.2.60: A family of exponentials The curves y = xeax are shown in the figu...
 7.2.61: Solid of revolution Find the volume of the solid generated when the...
 7.2.62: Between the sine and inverse sine Find the area of the region bound...
 7.2.63: Comparing volumes Let R be the region bounded by y = sin x and the ...
 7.2.64: Log integrals Use integration by parts to show that for m _ 1, L x...
 7.2.65: A useful integral a. Use integration by parts to show that if f _ i...
 7.2.66: Integrating inverse functions Assume that f has an inverse on its d...
 7.2.67: Integral of sec3 x Use integration by parts to show that L sec3 x d...
 7.2.68: Two useful exponential integrals Use integration by parts to derive...
 7.2.69: Oscillator displacements Suppose a mass on a spring that is slowed ...
 7.2.70: Find the error Suppose you evaluate L dx x using integration by par...
 7.2.71: Tabular integration Consider the integral 1f 1x2g1x2 dx, where f an...
 7.2.72: Practice with tabular integration Evaluate the following integrals ...
 7.2.73: Tabular integration extended Refer to Exercise 71. a. The following...
 7.2.74: Integrating derivatives Use integration by parts to show that if f ...
 7.2.75: An identity Show that if f has a continuous second derivative on 3a...
 7.2.76: An identity Show that if f and g have continuous second derivatives...
 7.2.77: Possible and impossible integrals Let In = 1xnex2 dx, where n is a...
 7.2.78: Looking ahead (to Chapter 9) Suppose that a function f has derivati...
Solutions for Chapter 7.2: Calculus: Early Transcendentals 2nd Edition
Full solutions for Calculus: Early Transcendentals  2nd Edition
ISBN: 9780321947345
Solutions for Chapter 7.2
Get Full SolutionsCalculus: Early Transcendentals was written by and is associated to the ISBN: 9780321947345. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 7.2 includes 78 full stepbystep solutions. Since 78 problems in chapter 7.2 have been answered, more than 61538 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 2.

Arccotangent function
See Inverse cotangent function.

Cube root
nth root, where n = 3 (see Principal nth root),

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

Equivalent vectors
Vectors with the same magnitude and direction.

Halfangle identity
Identity involving a trigonometric function of u/2.

Inverse variation
See Power function.

Invertible linear system
A system of n linear equations in n variables whose coefficient matrix has a nonzero determinant.

Logarithmic regression
See Natural logarithmic regression

Matrix element
Any of the real numbers in a matrix

Midpoint (on a number line)
For the line segment with endpoints a and b, a + b2

Natural logarithm
A logarithm with base e.

Polar coordinates
The numbers (r, ?) that determine a point’s location in a polar coordinate system. The number r is the directed distance and ? is the directed angle

Polar distance formula
The distance between the points with polar coordinates (r1, ?1 ) and (r2, ?2 ) = 2r 12 + r 22  2r1r2 cos 1?1  ?22

Semiminor axis
The distance from the center of an ellipse to a point on the ellipse along a line perpendicular to the major axis.

Sinusoidal regression
A procedure for fitting a curve y = a sin (bx + c) + d to a set of data

Standard form: equation of a circle
(x  h)2 + (y  k2) = r 2

Sum of a finite arithmetic series
Sn = na a1 + a2 2 b = n 2 32a1 + 1n  12d4,

Supply curve
p = ƒ(x), where x represents production and p represents price

Union of two sets A and B
The set of all elements that belong to A or B or both.

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