Using the Mean Value Theorem for Integrals In Exercises 45-50, find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the given interval. f ( x ) = 5 − 1 x , [ 1 , 4 ]
Using the Mean Value Theorem for Integrals In Exercises 45-50, find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the given interval. f ( x ) = 5 − 1 x , [ 1 , 4 ]
Solution Summary: The author explains how to calculate the value of c by the mean value theorem.
Using the Mean Value Theorem for Integrals In Exercises 45-50, find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the given interval.
f
(
x
)
=
5
−
1
x
,
[
1
,
4
]
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
The graph of the function f consists of the three line segments joining the points (0, 0), (2, −2), (6, 2), and (8, 3). The function F is defined by the integral F(x) (a) Sketch the graph of f. (b) Complete the table. (c) Find the extrema of F on the interval [0, 8]. (d) Determine all points of inflection of F on the interval (0, 8).
Algebra
Suppose that the function p(x) approximates the function f(x) with a maximum error of ε over the interval [a, b]. Then what is the error for the approximation of the integral [a,b] p(x)dx for the integral [a,b] f (x)dx.
Evaluate the definite integral
X
-1 1 + x² + x4
(a) [¹
1
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√x, (b) [¹² (x² + 3)(2x + 1)dx, (c) [²x²e²³ dæ
dx
-1
-1
222
Chapter 5 Solutions
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