 5.6.1: (a) If F (x) is an antiderivative for f(x), then baf(x) dx =(b) baF...
 5.6.2: (a) 20(3x2 2x) dx =(b) cos x dx =(c) 12 ln 50ex dx =(d) 1/21/211 x2...
 5.6.3: For the function f(x) = 3x2 2x and an interval [a, b],the point x g...
 5.6.4: The area of an oil spill is increasing at a rate of 25t ft2/st seco...
 5.6.5: 510 Find the area under the curve y = f(x) over the stated interval...
 5.6.6: 510 Find the area under the curve y = f(x) over the stated interval...
 5.6.7: 510 Find the area under the curve y = f(x) over the stated interval...
 5.6.8: 510 Find the area under the curve y = f(x) over the stated interval...
 5.6.9: 510 Find the area under the curve y = f(x) over the stated interval...
 5.6.10: 510 Find the area under the curve y = f(x) over the stated interval...
 5.6.11: 1112 Find all values of x in the stated interval that satisfyEquati...
 5.6.12: 1112 Find all values of x in the stated interval that satisfyEquati...
 5.6.13: 1330 Evaluate the integrals using Part 1 of the Fundamental Theorem...
 5.6.14: 1330 Evaluate the integrals using Part 1 of the Fundamental Theorem...
 5.6.15: 1330 Evaluate the integrals using Part 1 of the Fundamental Theorem...
 5.6.16: 1330 Evaluate the integrals using Part 1 of the Fundamental Theorem...
 5.6.17: 1330 Evaluate the integrals using Part 1 of the Fundamental Theorem...
 5.6.18: 1330 Evaluate the integrals using Part 1 of the Fundamental Theorem...
 5.6.19: 1330 Evaluate the integrals using Part 1 of the Fundamental Theorem...
 5.6.20: 1330 Evaluate the integrals using Part 1 of the Fundamental Theorem...
 5.6.21: 1330 Evaluate the integrals using Part 1 of the Fundamental Theorem...
 5.6.22: 1330 Evaluate the integrals using Part 1 of the Fundamental Theorem...
 5.6.23: 1330 Evaluate the integrals using Part 1 of the Fundamental Theorem...
 5.6.24: 1330 Evaluate the integrals using Part 1 of the Fundamental Theorem...
 5.6.25: 1330 Evaluate the integrals using Part 1 of the Fundamental Theorem...
 5.6.26: 1330 Evaluate the integrals using Part 1 of the Fundamental Theorem...
 5.6.27: 1330 Evaluate the integrals using Part 1 of the Fundamental Theorem...
 5.6.28: 1330 Evaluate the integrals using Part 1 of the Fundamental Theorem...
 5.6.29: 1330 Evaluate the integrals using Part 1 of the Fundamental Theorem...
 5.6.30: 1330 Evaluate the integrals using Part 1 of the Fundamental Theorem...
 5.6.31: 3134 Use Theorem 5.5.5 to evaluate the given integrals. (a) 112x 1...
 5.6.32: 3134 Use Theorem 5.5.5 to evaluate the given integrals. (a) 212 + ...
 5.6.33: 3134 Use Theorem 5.5.5 to evaluate the given integrals. (a) 11ex 1...
 5.6.34: 3134 Use Theorem 5.5.5 to evaluate the given integrals. (a) 33x2 1 ...
 5.6.35: 3536 A function f(x) is defined piecewise on an interval. Inthese e...
 5.6.36: 3536 A function f(x) is defined piecewise on an interval. Inthese e...
 5.6.37: 3740 TrueFalse Determine whether the statement is true orfalse. Exp...
 5.6.38: 3740 TrueFalse Determine whether the statement is true orfalse. Exp...
 5.6.39: 3740 TrueFalse Determine whether the statement is true orfalse. Exp...
 5.6.40: 3740 TrueFalse Determine whether the statement is true orfalse. Exp...
 5.6.41: 4144 Use a calculating utility to find the midpoint approximationof...
 5.6.42: 4144 Use a calculating utility to find the midpoint approximationof...
 5.6.43: 4144 Use a calculating utility to find the midpoint approximationof...
 5.6.44: 4144 Use a calculating utility to find the midpoint approximationof...
 5.6.45: 4548 Sketch the region described and find its area. The region unde...
 5.6.46: 4548 Sketch the region described and find its area. The region belo...
 5.6.47: 4548 Sketch the region described and find its area. The region unde...
 5.6.48: 4548 Sketch the region described and find its area. The region belo...
 5.6.49: 4952 Sketch the curve and find the total area between thecurve and ...
 5.6.50: 4952 Sketch the curve and find the total area between thecurve and ...
 5.6.51: 4952 Sketch the curve and find the total area between thecurve and ...
 5.6.52: 4952 Sketch the curve and find the total area between thecurve and ...
 5.6.53: A student wants to find the area enclosed by the graphs ofy = 1/1 x...
 5.6.54: Explain why the Fundamental Theorem of Calculus maybe applied witho...
 5.6.55: (a) If h(t) is the rate of change of a childs heightmeasured in inc...
 5.6.56: (a) Use a graphing utility to generate the graph off(x) = 1100 (x +...
 5.6.57: Define F (x) byF (x) = x1(3t2 3)dt(a) Use Part 2 of the Fundamental...
 5.6.58: Define F (x) byF (x) = x/4cos 2t dt(a) Use Part 2 of the Fundamenta...
 5.6.59: 5962 Use Part 2 of the Fundamental Theorem of Calculus tofind the d...
 5.6.60: 5962 Use Part 2 of the Fundamental Theorem of Calculus tofind the d...
 5.6.61: 5962 Use Part 2 of the Fundamental Theorem of Calculus tofind the d...
 5.6.62: 5962 Use Part 2 of the Fundamental Theorem of Calculus tofind the d...
 5.6.63: Let F (x) = x4t 2 + 9 dt. Find(a) F (4) (b) F(4) (c) F(4).64
 5.6.64: Let F (x) = x3tan1 t dt. Find(a) F (3) (b) F(3) (c) F(3).65
 5.6.65: Let F (x) = x0t 3t 2 + 7dt for <x< +.(a) Find the value of x where ...
 5.6.66: Use the plotting and numerical integration commands of aCAS to gene...
 5.6.67: (a) Over what open interval does the formulaF (x) = x1dttrepresent ...
 5.6.68: (a) Over what open interval does the formulaF (x) = x11t 2 9dtrepre...
 5.6.69: (a) Suppose that a reservoir supplies water to an industrialpark at...
 5.6.70: A traffic engineer monitors the rate at which cars enter themain hi...
 5.6.71: 7172 Evaluate each limit by interpreting it as a Riemann sumin whic...
 5.6.72: 7172 Evaluate each limit by interpreting it as a Riemann sumin whic...
 5.6.73: Prove the MeanValue Theorem for Integrals (Theorem5.6.2) by applyi...
 5.6.74: Writing Write a short paragraph that describes the variousways in w...
 5.6.75: Writing Let f denote a function that is continuous on aninterval [a...
Solutions for Chapter 5.6: THE FUNDAMENTAL THEOREM OF CALCULUS
Full solutions for Calculus: Early Transcendentals,  10th Edition
ISBN: 9780470647691
Solutions for Chapter 5.6: THE FUNDAMENTAL THEOREM OF CALCULUS
Get Full SolutionsCalculus: Early Transcendentals, was written by and is associated to the ISBN: 9780470647691. Chapter 5.6: THE FUNDAMENTAL THEOREM OF CALCULUS includes 75 full stepbystep solutions. Since 75 problems in chapter 5.6: THE FUNDAMENTAL THEOREM OF CALCULUS have been answered, more than 38616 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, , edition: 10. This expansive textbook survival guide covers the following chapters and their solutions.

Bias
A flaw in the design of a sampling process that systematically causes the sample to differ from the population with respect to the statistic being measured. Undercoverage bias results when the sample systematically excludes one or more segments of the population. Voluntary response bias results when a sample consists only of those who volunteer their responses. Response bias results when the sampling design intentionally or unintentionally influences the responses

Complements or complementary angles
Two angles of positive measure whose sum is 90°

Continuous function
A function that is continuous on its entire domain

Distance (on a number line)
The distance between real numbers a and b, or a  b

equation of a hyperbola
(x  h)2 a2  (y  k)2 b2 = 1 or (y  k)2 a2  (x  h)2 b2 = 1

equation of an ellipse
(x  h2) a2 + (y  k)2 b2 = 1 or (y  k)2 a2 + (x  h)2 b2 = 1

Fundamental
Theorem of Algebra A polynomial function of degree has n complex zeros (counting multiplicity).

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

Horizontal shrink or stretch
See Shrink, stretch.

Local maximum
A value ƒ(c) is a local maximum of ƒ if there is an open interval I containing c such that ƒ(x) < ƒ(c) for all values of x in I

Natural logarithmic regression
A procedure for fitting a logarithmic curve to a set of data.

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

Obtuse triangle
A triangle in which one angle is greater than 90°.

Product of functions
(ƒg)(x) = ƒ(x)g(x)

Random numbers
Numbers that can be used by researchers to simulate randomness in scientific studies (they are usually obtained from lengthy tables of decimal digits that have been generated by verifiably random natural phenomena).

Reference angle
See Reference triangle

Relation
A set of ordered pairs of real numbers.

Symmetric about the origin
A graph in which (x, y) is on the the graph whenever (x, y) is; or a graph in which (r, ?) or (r, ? + ?) is on the graph whenever (r, ?) is

Tree diagram
A visualization of the Multiplication Principle of Probability.

Vertex form for a quadratic function
ƒ(x) = a(x  h)2 + k