 6.4.1: For x = 0, 0.5, 1.0, 1.5, and 2.0, make a table of values for I(x) ...
 6.4.2: Assume that F (t) = sin t cos t and F(0) = 1. Find F(b) for b = 0, ...
 6.4.3: (a)  Continue the table of values for Si(x) = x 0 (sin t/t) dt on ...
 6.4.4: In Exercises 46, write an expression for the function, f(x), with t...
 6.4.5: In Exercises 46, write an expression for the function, f(x), with t...
 6.4.6: In Exercises 46, write an expression for the function, f(x), with t...
 6.4.7: In Exercises 710, let F(x) =  x 0 f(t) dt. Graph F(x) as a functio...
 6.4.8: In Exercises 710, let F(x) =  x 0 f(t) dt. Graph F(x) as a functio...
 6.4.9: In Exercises 710, let F(x) =  x 0 f(t) dt. Graph F(x) as a functio...
 6.4.10: In Exercises 710, let F(x) =  x 0 f(t) dt. Graph F(x) as a functio...
 6.4.11: Find the derivatives in Exercises 1116.
 6.4.12: Find the derivatives in Exercises 1116.
 6.4.13: Find the derivatives in Exercises 1116.
 6.4.14: Find the derivatives in Exercises 1116.
 6.4.15: Find the derivatives in Exercises 1116.
 6.4.16: Find the derivatives in Exercises 1116.
 6.4.17: Find intervals where the graph of F(x) =  x 0 et2 dt is concave up...
 6.4.18: Use properties of the function f(x) = xex to determine the number o...
 6.4.19: For 1921, let F(x) =  x 0 sin(t 2) dt
 6.4.20: For 1921, let F(x) =  x 0 sin(t 2) dt
 6.4.21: For 1921, let F(x) =  x 0 sin(t 2) dt
 6.4.22: Use Figure 6.28 to sketch a graph of F(x) =  x 0 f(t) dt. Label th...
 6.4.23: The graph of the derivative F of some function F is given in Figure...
 6.4.24: Let g(x) =  x 0 f(t) dt. Using Figure 6.30, find (a) g(0) (b) g (1...
 6.4.25: Let F(x) =  x 0 sin(2t) dt. (a) Evaluate F(). (b) Draw a sketch to...
 6.4.26: Let F(x) =  x 2 (1/ln t) dt for x 2. (a) Find F (x). (b) Is F incr...
 6.4.27: Let R(x) = , x 0 1 + t2 dt (a) Evaluate R(0) and determine if R is ...
 6.4.28: Suppose that f(x) is a continuous function and  b a f(t) dt = 0 fo...
 6.4.29: In 2930, find the value of the function with the given properties.
 6.4.30: In 2930, find the value of the function with the given properties.
 6.4.31: In 3134, estimate the value of each expression, given w(t) =  t 0 ...
 6.4.32: In 3134, estimate the value of each expression, given w(t) =  t 0 ...
 6.4.33: In 3134, estimate the value of each expression, given w(t) =  t 0 ...
 6.4.34: In 3134, estimate the value of each expression, given w(t) =  t 0 ...
 6.4.35: In 3538, use the chain rule to calculate the derivative.
 6.4.36: In 3538, use the chain rule to calculate the derivative.
 6.4.37: In 3538, use the chain rule to calculate the derivative.
 6.4.38: In 3538, use the chain rule to calculate the derivative.
 6.4.39: In 3942, find the given quantities. The error function, erf(x), is ...
 6.4.40: In 3942, find the given quantities. The error function, erf(x), is ...
 6.4.41: In 3942, find the given quantities. The error function, erf(x), is ...
 6.4.42: In 3942, find the given quantities. The error function, erf(x), is ...
 6.4.43: In 4345, explain what is wrong with the statement
 6.4.44: In 4345, explain what is wrong with the statement
 6.4.45: In 4345, explain what is wrong with the statement
 6.4.46: A function, F(x), constructed using the Second Fundamental Theorem ...
 6.4.47: A function G(x), constructed using the Second Fundamental Theorem o...
 6.4.48: Are the statements in 4853 true or false? Give an explanation for y...
 6.4.49: Are the statements in 4853 true or false? Give an explanation for y...
 6.4.50: Are the statements in 4853 true or false? Give an explanation for y...
 6.4.51: Are the statements in 4853 true or false? Give an explanation for y...
 6.4.52: Are the statements in 4853 true or false? Give an explanation for y...
 6.4.53: Are the statements in 4853 true or false? Give an explanation for y...
Solutions for Chapter 6.4: SECOND FUNDAMENTAL THEOREM OF CALCULUS
Full solutions for Calculus: Single Variable  6th Edition
ISBN: 9780470888643
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 34932 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 6.4: SECOND FUNDAMENTAL THEOREM OF CALCULUS includes 53 full stepbystep solutions. Calculus: Single Variable was written by and is associated to the ISBN: 9780470888643. This textbook survival guide was created for the textbook: Calculus: Single Variable , edition: 6.

Acute triangle
A triangle in which all angles measure less than 90°

Algebraic expression
A combination of variables and constants involving addition, subtraction, multiplication, division, powers, and roots

Associative properties
a + (b + c) = (a + b) + c, a(bc) = (ab)c.

Combinatorics
A branch of mathematics related to determining the number of elements of a set or the number of ways objects can be arranged or combined

Demand curve
p = g(x), where x represents demand and p represents price

Dependent variable
Variable representing the range value of a function (usually y)

Direction vector for a line
A vector in the direction of a line in threedimensional space

Equation
A statement of equality between two expressions.

Exponent
See nth power of a.

Inequality
A statement that compares two quantities using an inequality symbol

Inverse cosecant function
The function y = csc1 x

Linear factorization theorem
A polynomial ƒ(x) of degree n > 0 has the factorization ƒ(x) = a(x1  z1) 1x  i z 22 Á 1x  z n where the z1 are the zeros of ƒ

Midpoint (in a coordinate plane)
For the line segment with endpoints (a,b) and (c,d), (aa + c2 ,b + d2)

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

Pythagorean identities
sin2 u + cos2 u = 1, 1 + tan2 u = sec2 u, and 1 + cot2 u = csc2 u

Quotient of functions
a ƒ g b(x) = ƒ(x) g(x) , g(x) ? 0

Range screen
See Viewing window.

Second quartile
See Quartile.

Sum of complex numbers
(a + bi) + (c + di) = (a + c) + (b + d)i

Time plot
A line graph in which time is measured on the horizontal axis.