Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.2: Derivatives Of Products And Quotients
Problem 36E
Related questions
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()
respectively, and that c is a constant. Then:
(a) A constant factor can be moved through an integral sign; that is,
| ef(x) de = cF(x) +C.
(b) An antiderivative of a sum is the sum of the antiderivatives;
that is,
Su
(x) + g(x)] dx = F(x)+ G(x)+ C.
(c) An antiderivative of a difference is the difference of the
antiderivatives; that is,
|If (#) – g(x)] dr = F(x) – G(æ) + C.
g*+1
The power rule:
x" dx
+ C,r + -1.
r+1
NOTE: Enter the exact answer.
6
dy
+C
Lyš](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff8598701-1ea9-4df2-9201-44e4586a46ad%2F272f33a9-09be-4fa8-ab07-2a94b8e9a4f4%2F4phigrn_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()
respectively, and that c is a constant. Then:
(a) A constant factor can be moved through an integral sign; that is,
| ef(x) de = cF(x) +C.
(b) An antiderivative of a sum is the sum of the antiderivatives;
that is,
Su
(x) + g(x)] dx = F(x)+ G(x)+ C.
(c) An antiderivative of a difference is the difference of the
antiderivatives; that is,
|If (#) – g(x)] dr = F(x) – G(æ) + C.
g*+1
The power rule:
x" dx
+ C,r + -1.
r+1
NOTE: Enter the exact answer.
6
dy
+C
Lyš
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 1 images
Recommended textbooks for you
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Functions and Change: A Modeling Approach to Coll…
Algebra
ISBN:
9781337111348
Author:
Bruce Crauder, Benny Evans, Alan Noell
Publisher:
Cengage Learning
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Functions and Change: A Modeling Approach to Coll…
Algebra
ISBN:
9781337111348
Author:
Bruce Crauder, Benny Evans, Alan Noell
Publisher:
Cengage Learning
