 6.4.1: For x = 0, 0.5, 1.0, 1.5, and 2.0, make a table of valuesfor I(x) =...
 6.4.2: Assume that F(t) = sin t cos t and F(0) = 1. FindF(b) for b = 0, 0....
 6.4.3: (a)Continue the table of values for Si(x) = x0 (sin t/t) dt on pag...
 6.4.4: In Exercises 46, write an expression for the function, f(x),with th...
 6.4.5: In Exercises 46, write an expression for the function, f(x),with th...
 6.4.6: In Exercises 46, write an expression for the function, f(x),with th...
 6.4.7: In Exercises 710, let F(x) =  x0 f(t) dt. Graph F(x) as afunction ...
 6.4.8: In Exercises 710, let F(x) =  x0 f(t) dt. Graph F(x) as afunction ...
 6.4.9: In Exercises 710, let F(x) =  x0 f(t) dt. Graph F(x) as afunction ...
 6.4.10: In Exercises 710, let F(x) =  x0 f(t) dt. Graph F(x) as afunction ...
 6.4.11: Find the derivatives in Exercises 1116.ddx , x0cos(t2) dt
 6.4.12: Find the derivatives in Exercises 1116.ddt , t4sin(x) dx
 6.4.13: Find the derivatives in Exercises 1116.ddx , x1(1 + t)200 dt
 6.4.14: Find the derivatives in Exercises 1116.ddx , x2ln(t2 + 1) dt
 6.4.15: Find the derivatives in Exercises 1116.ddx , x0.5arctan(t2) dt
 6.4.16: Find the derivatives in Exercises 1116.ddx"Si(x2)#
 6.4.17: Find intervals where the graph of F(x) =  x0 et2dt isconcave up an...
 6.4.18: Use properties of the function f(x) = xex to determinethe number of...
 6.4.19: For 1921, let F(x) =  x0 sin(t2) dt.Approximate F(x) for x = 0, 0....
 6.4.20: For 1921, let F(x) =  x0 sin(t2) dt.Using a graph of F(x), decide ...
 6.4.21: For 1921, let F(x) =  x0 sin(t2) dt.Does F(x) have a maximum value...
 6.4.22: Use Figure 6.28 to sketch a graph of F(x) =  x0 f(t) dt.Label the ...
 6.4.23: The graph of the derivative F of some function F isgiven in Figure ...
 6.4.24: Let g(x) =  x0 f(t) dt. Using Figure 6.30, find(a) g(0) (b) g(1)(c...
 6.4.25: Let F(x) =  x0 sin(2t) dt.(a) Evaluate F().(b) Draw a sketch to ex...
 6.4.26: Let F(x) =  x2 (1/ln t) dt for x 2.(a) Find F(x).(b) Is F increasi...
 6.4.27: Let R(x) = , x01 + t2 dt(a) Evaluate R(0) and determine if R is an ...
 6.4.28: Suppose that f(x) is a continuous function and ba f(t) dt = 0 for ...
 6.4.29: In 2930, find the value of the function with thegiven properties.F(...
 6.4.30: In 2930, find the value of the function with thegiven properties.G(...
 6.4.31: In 3134, estimate the value of each expression,given w(t) =  t0 q(...
 6.4.32: In 3134, estimate the value of each expression,given w(t) =  t0 q(...
 6.4.33: In 3134, estimate the value of each expression,given w(t) =  t0 q(...
 6.4.34: In 3134, estimate the value of each expression,given w(t) =  t0 q(...
 6.4.35: In 3538, use the chain rule to calculate the derivativeddx , x20ln(...
 6.4.36: In 3538, use the chain rule to calculate the derivativeddt , sin t1...
 6.4.37: In 3538, use the chain rule to calculate the derivativeddt , 42tsin...
 6.4.38: In 3538, use the chain rule to calculate the derivativeddx , x2x2et2dt
 6.4.39: In 3942, find the given quantities. The error function,erf(x), is d...
 6.4.40: In 3942, find the given quantities. The error function,erf(x), is d...
 6.4.41: In 3942, find the given quantities. The error function,erf(x), is d...
 6.4.42: In 3942, find the given quantities. The error function,erf(x), is d...
 6.4.43: In 4345, explain what is wrong with the statement.ddx , 50t2 dt = x2.
 6.4.44: In 4345, explain what is wrong with the statement.F(x) = , x2t2 dt ...
 6.4.45: In 4345, explain what is wrong with the statement.For the function ...
 6.4.46: In 4647, give an example ofA function, F(x), constructed using the ...
 6.4.47: In 4647, give an example ofA function G(x), constructed using the S...
 6.4.48: Are the statements in 4853 true or false? Give anexplanation for yo...
 6.4.49: Are the statements in 4853 true or false? Give anexplanation for yo...
 6.4.50: Are the statements in 4853 true or false? Give anexplanation for yo...
 6.4.51: Are the statements in 4853 true or false? Give anexplanation for yo...
 6.4.52: Are the statements in 4853 true or false? Give anexplanation for yo...
 6.4.53: Are the statements in 4853 true or false? Give anexplanation for yo...
Solutions for Chapter 6.4: SECOND FUNDAMENTAL THEOREM OF CALCULUS
Full solutions for Calculus: Single and Multivariable  6th Edition
ISBN: 9780470888612
Solutions for Chapter 6.4: SECOND FUNDAMENTAL THEOREM OF CALCULUS
Get Full SolutionsSince 53 problems in chapter 6.4: SECOND FUNDAMENTAL THEOREM OF CALCULUS have been answered, more than 43276 students have viewed full stepbystep solutions from this chapter. Chapter 6.4: SECOND FUNDAMENTAL THEOREM OF CALCULUS includes 53 full stepbystep solutions. This textbook survival guide was created for the textbook: Calculus: Single and Multivariable , edition: 6. This expansive textbook survival guide covers the following chapters and their solutions. Calculus: Single and Multivariable was written by and is associated to the ISBN: 9780470888612.

Absolute value of a complex number
The absolute value of the complex number z = a + b is given by ?a2+b2; also, the length of the segment from the origin to z in the complex plane.

Average rate of change of ƒ over [a, b]
The number ƒ(b)  ƒ(a) b  a, provided a ? b.

Complex conjugates
Complex numbers a + bi and a  bi

Domain of a function
The set of all input values for a function

Doubleblind experiment
A blind experiment in which the researcher gathering data from the subjects is not told which subjects have received which treatment

Heron’s formula
The area of ¢ABC with semiperimeter s is given by 2s1s  a21s  b21s  c2.

Jump discontinuity at x a
limx:a  ƒ1x2 and limx:a + ƒ1x2 exist but are not equal

Leading coefficient
See Polynomial function in x

Leastsquares line
See Linear regression line.

Magnitude of an arrow
The magnitude of PQ is the distance between P and Q

Objective function
See Linear programming problem.

Parametric equations
Equations of the form x = ƒ(t) and y = g(t) for all t in an interval I. The variable t is the parameter and I is the parameter interval.

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.

Quotient rule of logarithms
logb a R S b = logb R  logb S, R > 0, S > 0

Radius
The distance from a point on a circle (or a sphere) to the center of the circle (or the sphere).

Resistant measure
A statistical measure that does not change much in response to outliers.

Scalar
A real number.

Sequence
See Finite sequence, Infinite sequence.

Standard unit vectors
In the plane i = <1, 0> and j = <0,1>; in space i = <1,0,0>, j = <0,1,0> k = <0,0,1>

Statistic
A number that measures a quantitative variable for a sample from a population.