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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Question
![Evaluate the integral by applying the following theorems
and the power rule appropriately.
Suppose that F(x) and G(x) are antiderivatives of f(x) and g(x)
respectively, and that c is a constant. Then:
(a) A constant factor can be moved through an integral sign; that is,
fef (2) dr =
cF(x)+ C.
(b) An antiderivative of a sum is the sum of the antiderivatives;
that is,
|[S (x) + g(x)] da = F(x)+ G(x)+ C.
(c) An antiderivative of a difference is the difference of the
antiderivatives; that is,
|S(z) – 9(z)) dz =
F(x) – G(x)+ C.
x*+1
+C,r+ -1.
The power rule:
x" dx
r +1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fed2042a4-f8f6-45e2-8d46-73bceccac15f%2F42436dd7-f090-427c-a068-8dfbfe0cc84e%2Fqvx4on_processed.png&w=3840&q=75)
Transcribed Image Text:Evaluate the integral by applying the following theorems
and the power rule appropriately.
Suppose that F(x) and G(x) are antiderivatives of f(x) and g(x)
respectively, and that c is a constant. Then:
(a) A constant factor can be moved through an integral sign; that is,
fef (2) dr =
cF(x)+ C.
(b) An antiderivative of a sum is the sum of the antiderivatives;
that is,
|[S (x) + g(x)] da = F(x)+ G(x)+ C.
(c) An antiderivative of a difference is the difference of the
antiderivatives; that is,
|S(z) – 9(z)) dz =
F(x) – G(x)+ C.
x*+1
+C,r+ -1.
The power rule:
x" dx
r +1
Transcribed Image Text:9.
Vỹ +
dy
+C
-
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