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, [ cf(x) dx = cF(x) + C. (b) An antiderivative of a sum is the sum of the antiderivatives; that is, [[f(x) + g(x)] dx = F(x) + G(x) + C. (c) An antiderivative of a difference is the difference of the antiderivatives; that is, [[f(x) − g(x)] dx = F(x) − G(x) + C. e fæ² da x²+1 The power rule: x dx = +C, r = -1. r+1 NOTE: Enter the exact answer. S[x- x−³ − 3xổ + 5x²| dx = - +C
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, [ cf(x) dx = cF(x) + C. (b) An antiderivative of a sum is the sum of the antiderivatives; that is, [[f(x) + g(x)] dx = F(x) + G(x) + C. (c) An antiderivative of a difference is the difference of the antiderivatives; that is, [[f(x) − g(x)] dx = F(x) − G(x) + C. e fæ² da x²+1 The power rule: x dx = +C, r = -1. r+1 NOTE: Enter the exact answer. S[x- x−³ − 3xổ + 5x²| dx = - +C
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
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Chapter2: Functions And Graphs
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Problem 22E: Find the constant of proportionality. z is directly proportional to the sum of x and y. If x=2 and...
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![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,
[ cf(x) dx = cF(x) + C.
(b) An antiderivative of a sum is the sum of the antiderivatives;
that is,
[[f(x) + g(x)] dx = F(x) + G(x) + C.
(c) An antiderivative of a difference is the difference of the
antiderivatives; that is,
[[f(x) − g(x)] dx = F(x) − G(x) + C.
e fæ² da
x²+1
The power rule: x dx =
+C, r = -1.
r+1
NOTE: Enter the exact answer.
S[x-
x−³ − 3xổ + 5x²| dx =
-
+C](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7fc70597-7de9-4d95-bb98-47fe79963ee6%2Ff6e4e352-6408-410d-957a-0ec31c5f701f%2F8lqab32_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,
[ cf(x) dx = cF(x) + C.
(b) An antiderivative of a sum is the sum of the antiderivatives;
that is,
[[f(x) + g(x)] dx = F(x) + G(x) + C.
(c) An antiderivative of a difference is the difference of the
antiderivatives; that is,
[[f(x) − g(x)] dx = F(x) − G(x) + C.
e fæ² da
x²+1
The power rule: x dx =
+C, r = -1.
r+1
NOTE: Enter the exact answer.
S[x-
x−³ − 3xổ + 5x²| dx =
-
+C
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