Let g be a differentiable function of x, and let the range of g be an interval [a, b]. Let f be a function defined on [a, b], F is an antiderivative of f on [a, b] and u = g(x). Then the chain rule for antidifferentiation is defined as 1. a. ff(g(x))dx = f f(u)du = F(u) + C = F(g(x)) +C F(u) + C = F(g'(x)) +C = F(u) + C =F(g'(x)) + C = F(g(x)) + C %3D b. ff(g'(x))dx = f f(u)du c. Sf(g'(x))g(x)dx f f(u)du 000 d. Sf(g (x))g'(x)dx = S f(u)du %3D F(u) + C = 2. In evaluatingf x (5+ 2x2)3 dx, what would be the substitution for u? a. х b..5+ 2x2 c. x(5+ 2x2) d. x(5+ 2x2)3 no Evaluate f x (5 + 2x2)³ dx. (5 + 2x2) + C b. (5+ 2x2)* + C 3. a. 8. (5 + 2x2) +C d. (5+ 2x2) + C c. 12 16
Let g be a differentiable function of x, and let the range of g be an interval [a, b]. Let f be a function defined on [a, b], F is an antiderivative of f on [a, b] and u = g(x). Then the chain rule for antidifferentiation is defined as 1. a. ff(g(x))dx = f f(u)du = F(u) + C = F(g(x)) +C F(u) + C = F(g'(x)) +C = F(u) + C =F(g'(x)) + C = F(g(x)) + C %3D b. ff(g'(x))dx = f f(u)du c. Sf(g'(x))g(x)dx f f(u)du 000 d. Sf(g (x))g'(x)dx = S f(u)du %3D F(u) + C = 2. In evaluatingf x (5+ 2x2)3 dx, what would be the substitution for u? a. х b..5+ 2x2 c. x(5+ 2x2) d. x(5+ 2x2)3 no Evaluate f x (5 + 2x2)³ dx. (5 + 2x2) + C b. (5+ 2x2)* + C 3. a. 8. (5 + 2x2) +C d. (5+ 2x2) + C c. 12 16
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
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Chapter1: Functions And Models
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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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![Let g be a differentiable function ofx, and let the range of g be an interval [a, b].
Let f be a function defined on [a, b], F is an antiderivative of f on [a, b] and u =
g(x). Then the chain rule for antidifferentiation is defined as
1.
a. ff(g(x))dx = S f(u)du
b. f(g'(x))dx = f f(u)du
c. Sf(g'(x))g(x)dx f f(u)du
t0009 d. Sf(g(x))g'(x)dx = S f(u)du s
F(u) +C = F(g(x)) + C
F (u) + C = F(gʻ(x)) + C
F(u) + C = F(g'(x)) + C
F(u) + C = F(g(x)) +C
%3D
%3D
%3D
2. In evaluatingf x (5+ 2x²)3 dx, what would be the substitution for u?
a. х
b..5+2x2
c. x(5+ 2x²)
d. x(5+ 2x2)3
no
3. Evaluate f x (5+ 2x2)3 dx.
a. (5+ 2x2)' + C
b.(5+ 2x2)* + C
c. (5+ 2x2)* + C
d. (5 + 2x2)* + C
16](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F00323904-e72f-44a6-8fd7-77e1566b8d91%2F3f4f7a26-95a0-4b6e-a1e9-0a68cdb01166%2Fk3fwf1_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let g be a differentiable function ofx, and let the range of g be an interval [a, b].
Let f be a function defined on [a, b], F is an antiderivative of f on [a, b] and u =
g(x). Then the chain rule for antidifferentiation is defined as
1.
a. ff(g(x))dx = S f(u)du
b. f(g'(x))dx = f f(u)du
c. Sf(g'(x))g(x)dx f f(u)du
t0009 d. Sf(g(x))g'(x)dx = S f(u)du s
F(u) +C = F(g(x)) + C
F (u) + C = F(gʻ(x)) + C
F(u) + C = F(g'(x)) + C
F(u) + C = F(g(x)) +C
%3D
%3D
%3D
2. In evaluatingf x (5+ 2x²)3 dx, what would be the substitution for u?
a. х
b..5+2x2
c. x(5+ 2x²)
d. x(5+ 2x2)3
no
3. Evaluate f x (5+ 2x2)3 dx.
a. (5+ 2x2)' + C
b.(5+ 2x2)* + C
c. (5+ 2x2)* + C
d. (5 + 2x2)* + C
16
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