The antiderivative of f(x), denoted by F(x), exhibits an odd symmetry i.e., it satisfies the property F( – x) = - F(x)· If / f(x)dr=K, 0

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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The antiderivative of f(x), denoted by F(x), exhibits an odd symmetry i.e., it satisfies the property F( -x)= - F(x). If /
f(x) dx =K, 0<a<b• determine which of the following is true.
[Assume both f(x) and F(x) are defined for all real values of x.]
1+x•f(x)
a
dx =K(-a+b) + In-
* -a 1+x· f(x)
a
-dx =K+ In-
b
-b
• -a 1+x•f(x)
dx = - K+ In-
-b
'1+x•f(x)
dx =
--K(-a+b) + In
-b
Transcribed Image Text:The antiderivative of f(x), denoted by F(x), exhibits an odd symmetry i.e., it satisfies the property F( -x)= - F(x). If / f(x) dx =K, 0<a<b• determine which of the following is true. [Assume both f(x) and F(x) are defined for all real values of x.] 1+x•f(x) a dx =K(-a+b) + In- * -a 1+x· f(x) a -dx =K+ In- b -b • -a 1+x•f(x) dx = - K+ In- -b '1+x•f(x) dx = --K(-a+b) + In -b
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