 4.1: In Exercises I and 2. use the Hinph of / ' to sketch a "iraph of/. ...
 4.2: In Exercises I and 2. use the Hinph of / ' to sketch a "iraph of/. ...
 4.3: In Exercises 38, Cind the indelinite integral. (2.V + v  l),/.v
 4.4: In Exercises 38, Cind the indelinite integral. 2 3x dx
 4.5: In Exercises 38, Cind the indelinite integral. x3 + 1 x3 dx
 4.6: In Exercises 38, Cind the indelinite integral. ^i^iiiI.,.
 4.7: In Exercises 38, Cind the indelinite integral. /(4.V  3 sin a)
 4.8: In Exercises 38, Cind the indelinite integral. 15 cos.v  2 sec a...
 4.9: Eind the particular solution of the differential equation /'(a) = ...
 4.10: Eind the particular solution ol the differential equation /"(a) = 6...
 4.11: Velocity and Acceleration An aiiplane taking off from a runway trav...
 4.12: Velocity ami Acceleration The speed of a car traveling in a straigh...
 4.13: Velocity and Acceleration .A ball is thrown verticalK upward from g...
 4.14: Velocity and Acceleration Repeat E.xercise 13 for an initial veloci...
 4.15: Write in sigma notation (a) the sum of the fust ten positive odd in...
 4.16: Hxaluate each sum for a, = 2. a, =  I. .v, = 5. .Vj = 3, and .V, =...
 4.17: In F.xercises 17 and IS, use upper and lower sums to approxi mate ...
 4.18: In F.xercises 17 and IS, use upper and lower sums to approxi mate ...
 4.19: In Exercises 1922, use the limit process to llnd the area of the r...
 4.20: In Exercises 1922, use the limit process to llnd the area of the r...
 4.21: In Exercises 1922, use the limit process to llnd the area of the r...
 4.22: In Exercises 1922, use the limit process to llnd the area of the r...
 4.23: L se the limit process to find the area ol the region bounded b> A ...
 4.24: Consider the region bounded by y = m\. y = 0. .v = 0. and A = /). (...
 4.25: In P^xercises 25 and 26, exprtss the limit as a definite integral o...
 4.26: In P^xercises 25 and 26, exprtss the limit as a definite integral o...
 4.27: In Kxereises 27 and 28. sketeh the refjlon whose area is given by t...
 4.28: In Kxereises 27 and 28. sketeh the refjlon whose area is given by t...
 4.29: In Exercises 29 and 30, use the given values to evaluate each defin...
 4.30: In Exercises 29 and 30, use the given values to evaluate each defin...
 4.31: In Exercises 31 and 32, select the correct value of the definite in...
 4.32: In Exercises 31 and 32, select the correct value of the definite in...
 4.33: In Exercises 33 tO, use the Eundamental Theorem of Calculus to eval...
 4.34: In Exercises 33 tO, use the Eundamental Theorem of Calculus to eval...
 4.35: In Exercises 33 tO, use the Eundamental Theorem of Calculus to eval...
 4.36: In Exercises 33 tO, use the Eundamental Theorem of Calculus to eval...
 4.37: In Exercises 33 tO, use the Eundamental Theorem of Calculus to eval...
 4.38: In Exercises 33 tO, use the Eundamental Theorem of Calculus to eval...
 4.39: In Exercises 33 tO, use the Eundamental Theorem of Calculus to eval...
 4.40: In Exercises 33 tO, use the Eundamental Theorem of Calculus to eval...
 4.41: In Exercises 4146, sketch the graph of the region whose area is gi...
 4.42: In Exercises 4146, sketch the graph of the region whose area is gi...
 4.43: In Exercises 4146, sketch the graph of the region whose area is gi...
 4.44: In Exercises 4146, sketch the graph of the region whose area is gi...
 4.45: In Exercises 4146, sketch the graph of the region whose area is gi...
 4.46: In Exercises 4146, sketch the graph of the region whose area is gi...
 4.47: In Exercises 47 and 48, sketch the region bounded by the graphs of ...
 4.48: In Exercises 47 and 48, sketch the region bounded by the graphs of ...
 4.49: In Exercises 49 and 50, find the average value of the function over...
 4.50: In Exercises 49 and 50, find the average value of the function over...
 4.51: In Exercises 5154, use the Second Fundamental Theorem of Calculus ...
 4.52: In Exercises 5154, use the Second Fundamental Theorem of Calculus ...
 4.53: In Exercises 5154, use the Second Fundamental Theorem of Calculus ...
 4.54: In Exercises 5154, use the Second Fundamental Theorem of Calculus ...
 4.55: In Exercises 5568. find the indefinite integral. (a + 1)''
 4.56: In Exercises 5568. find the indefinite integral. I I A +  I J.V
 4.57: In Exercises 5568. find the indefinite integral. X + 3
 4.58: In Exercises 5568. find the indefinite integral. v^ a' + 3
 4.59: In Exercises 5568. find the indefinite integral. v( 1  ixf
 4.60: In Exercises 5568. find the indefinite integral. A + 3 (.V + 6.V  5
 4.61: In Exercises 5568. find the indefinite integral. sin 'a cos A dx
 4.62: In Exercises 5568. find the indefinite integral.A sin 3a
 4.63: In Exercises 5568. find the indefinite integral. X ' 1  cos
 4.64: In Exercises 5568. find the indefinite integral. ^;^^,/v
 4.65: In Exercises 5568. find the indefinite integral.Ian" .v sec .v dx...
 4.66: In Exercises 5568. find the indefinite integral. sec 2.\ tan 2.v
 4.67: In Exercises 5568. find the indefinite integral. 11+ sec TT x) se...
 4.68: In Exercises 5568. find the indefinite integral. cut' a CSC" a da
 4.69: In Exercises 6976, evaluale the deiinite integral. Use a graphing ...
 4.70: In Exercises 6976, evaluale the deiinite integral. Use a graphing ...
 4.71: In Exercises 6976, evaluale the deiinite integral. Use a graphing ...
 4.72: In Exercises 6976, evaluale the deiinite integral. Use a graphing ...
 4.73: In Exercises 6976, evaluale the deiinite integral. Use a graphing ...
 4.74: In Exercises 6976, evaluale the deiinite integral. Use a graphing ...
 4.75: In Exercises 6976, evaluale the deiinite integral. Use a graphing ...
 4.76: In Exercises 6976, evaluale the deiinite integral. Use a graphing ...
 4.77: Probability In Exercises 77 and 78. the function /(.v) = Aa'MI  .v...
 4.78: Probability In Exercises 77 and 78. the function /(.v) = Aa'MI  .v...
 4.79: Suppose that gas where p is the dollar price per gallon and / is th...
 4.80: Respiratnry Cycle After exercising for a lew ininules. a person has...
 4.81: I" Exercises 8184, use the Trape/.oidal Rule and Simpson's Rule wi...
 4.82: I" Exercises 8184, use the Trape/.oidal Rule and Simpson's Rule wi...
 4.83: I" Exercises 8184, use the Trape/.oidal Rule and Simpson's Rule wi...
 4.84: I" Exercises 8184, use the Trape/.oidal Rule and Simpson's Rule wi...
 4.85: Let / = I /(v),/> where / is shown in the figure. l,et Lint and A'(...
Solutions for Chapter 4: Integration
Full solutions for Calculus of A Single Variable  7th Edition
ISBN: 9780618149162
Solutions for Chapter 4: Integration
Get Full SolutionsCalculus of A Single Variable was written by and is associated to the ISBN: 9780618149162. Chapter 4: Integration includes 85 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 85 problems in chapter 4: Integration have been answered, more than 23606 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Calculus of A Single Variable, edition: 7.

Blind experiment
An experiment in which subjects do not know if they have been given an active treatment or a placebo

Direct variation
See Power function.

Directed line segment
See Arrow.

Distance (in a coordinate plane)
The distance d(P, Q) between P(x, y) and Q(x, y) d(P, Q) = 2(x 1  x 2)2 + (y1  y2)2

Eccentricity
A nonnegative number that specifies how offcenter the focus of a conic is

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

Factored form
The left side of u(v + w) = uv + uw.

Imaginary axis
See Complex plane.

Median (of a data set)
The middle number (or the mean of the two middle numbers) if the data are listed in order.

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

nth root of a complex number z
A complex number v such that vn = z

Opposite
See Additive inverse of a real number and Additive inverse of a complex number.

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

Rectangular coordinate system
See Cartesian coordinate system.

Reflection
Two points that are symmetric with respect to a lineor a point.

Reflexive property of equality
a = a

Scientific notation
A positive number written as c x 10m, where 1 ? c < 10 and m is an integer.

Sinusoid
A function that can be written in the form f(x) = a sin (b (x  h)) + k or f(x) = a cos (b(x  h)) + k. The number a is the amplitude, and the number h is the phase shift.

Solve a triangle
To find one or more unknown sides or angles of a triangle

yaxis
Usually the vertical coordinate line in a Cartesian coordinate system with positive direction up, pp. 12, 629.