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. - da - x7+1 r+1 » / 20² NOTE: Enter the exact answer. The power rule: x" dx = 7 +]dy = SH - √5 + + C, r = -1. +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. - da - x7+1 r+1 » / 20² NOTE: Enter the exact answer. The power rule: x" dx = 7 +]dy = SH - √5 + + C, r = -1. +C
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter2: Functions And Graphs
Section2.6: Proportion And Variation
Problem 18E
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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) — 9(x)] da = F(x) − G(x) + C.
x²+1
r+1
[₂
NOTE: Enter the exact answer.
The power rule:
S# -*
x dx =
7
3y + dy =
√y
+ C,r-1.
+C](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F11df6d29-f242-4e84-af0f-c93e432e2f29%2Fc259e60d-ff09-43b9-9517-85c931ad6df0%2Ftx5wbyv_processed.jpeg&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) — 9(x)] da = F(x) − G(x) + C.
x²+1
r+1
[₂
NOTE: Enter the exact answer.
The power rule:
S# -*
x dx =
7
3y + dy =
√y
+ C,r-1.
+C
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