①Find the antiderivative F(x) of each function f(x) : a) f(x) = 4x² + 5√x-. b) f(x) = (-3x + cosx. Points ② Evaluate the integral: a) (3x²+2 dx b-) √x=13+x²/3 dx 2 points χε ③ Solve the Initial Value Problema: f'(x) = x-3 , f(1)=1 2 pts.' 5 ④⑦a) Evchats the integral uring area formula: Sitios de (4) Evaluate b). Find the average value of fox) = 6-2x over [0,3] (Hint: Draw the graph of the function over [43]. ⑤a) Give a clear statement of the Fundamental Theorem 5 parts 2+2 points. of Calculus, b) Use FTC1 to find the derivative: d x ( √19-y² dy c) " d dx Sinx Ex S√\\-+² dt. (6) a) Give a clear statement of FTC2 0 2+ 2 FTC2: (+²=-9X4-+³) al b). Evaluate the definite integral by using FTCZ: 2 7 Use a suitable change of variables to determine the indefinite integral 99 a) S x (1-x)" dx : b) {(x-5)4dx c) (sinto usodo (⑧a) Use integration by parts to find the integral. i) Sx cosx dx EXTRA (i) Slux. lux dx. b). Evaluate the trigonometric integrals: i) Scos³x sin³x dx (i). (cos³x dx. 2+2 12+2 E CREDIT. Use trigonometric substitution to solve S√36-72 dx 1+3 3 pts. 13
①Find the antiderivative F(x) of each function f(x) : a) f(x) = 4x² + 5√x-. b) f(x) = (-3x + cosx. Points ② Evaluate the integral: a) (3x²+2 dx b-) √x=13+x²/3 dx 2 points χε ③ Solve the Initial Value Problema: f'(x) = x-3 , f(1)=1 2 pts.' 5 ④⑦a) Evchats the integral uring area formula: Sitios de (4) Evaluate b). Find the average value of fox) = 6-2x over [0,3] (Hint: Draw the graph of the function over [43]. ⑤a) Give a clear statement of the Fundamental Theorem 5 parts 2+2 points. of Calculus, b) Use FTC1 to find the derivative: d x ( √19-y² dy c) " d dx Sinx Ex S√\\-+² dt. (6) a) Give a clear statement of FTC2 0 2+ 2 FTC2: (+²=-9X4-+³) al b). Evaluate the definite integral by using FTCZ: 2 7 Use a suitable change of variables to determine the indefinite integral 99 a) S x (1-x)" dx : b) {(x-5)4dx c) (sinto usodo (⑧a) Use integration by parts to find the integral. i) Sx cosx dx EXTRA (i) Slux. lux dx. b). Evaluate the trigonometric integrals: i) Scos³x sin³x dx (i). (cos³x dx. 2+2 12+2 E CREDIT. Use trigonometric substitution to solve S√36-72 dx 1+3 3 pts. 13
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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Please answer questions 1-9. This is not graded just a review.
![①Find the antiderivative F(x) of each function f(x) :
a) f(x) = 4x² + 5√x-.
b) f(x) = (-3x + cosx.
Points
② Evaluate the integral:
a) (3x²+2 dx
b-) √x=13+x²/3 dx
2
points
χε
③ Solve the Initial Value Problema:
f'(x) = x-3
,
f(1)=1
2
pts.'
5
④⑦a) Evchats the integral uring area formula: Sitios de
(4) Evaluate
b). Find the average value of fox) = 6-2x over [0,3]
(Hint: Draw the graph of the function over [43].
⑤a) Give a clear statement of the Fundamental Theorem
5
parts
2+2
points.
of Calculus,
b) Use FTC1 to find the derivative: d x ( √19-y² dy
c)
"
d
dx
Sinx
Ex S√\\-+² dt.
(6) a) Give a clear statement of FTC2
0
2+
2
FTC2: (+²=-9X4-+³) al
b). Evaluate the definite integral by using FTCZ:
2
7 Use a suitable change of variables to determine the
indefinite integral
99
a) S x (1-x)" dx
:
b) {(x-5)4dx c) (sinto usodo
(⑧a) Use integration by parts to find the integral.
i) Sx cosx dx
EXTRA
(i) Slux.
lux dx.
b). Evaluate the trigonometric integrals:
i) Scos³x sin³x dx
(i). (cos³x dx.
2+2
12+2
E CREDIT. Use trigonometric substitution to solve S√36-72 dx
1+3
3
pts.
13](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fabb39053-8adb-40a8-a5cf-59042daf8b2e%2Fe99238e3-a0f0-4962-a701-e5b98fe54751%2Fwmv5yrg_processed.png&w=3840&q=75)
Transcribed Image Text:①Find the antiderivative F(x) of each function f(x) :
a) f(x) = 4x² + 5√x-.
b) f(x) = (-3x + cosx.
Points
② Evaluate the integral:
a) (3x²+2 dx
b-) √x=13+x²/3 dx
2
points
χε
③ Solve the Initial Value Problema:
f'(x) = x-3
,
f(1)=1
2
pts.'
5
④⑦a) Evchats the integral uring area formula: Sitios de
(4) Evaluate
b). Find the average value of fox) = 6-2x over [0,3]
(Hint: Draw the graph of the function over [43].
⑤a) Give a clear statement of the Fundamental Theorem
5
parts
2+2
points.
of Calculus,
b) Use FTC1 to find the derivative: d x ( √19-y² dy
c)
"
d
dx
Sinx
Ex S√\\-+² dt.
(6) a) Give a clear statement of FTC2
0
2+
2
FTC2: (+²=-9X4-+³) al
b). Evaluate the definite integral by using FTCZ:
2
7 Use a suitable change of variables to determine the
indefinite integral
99
a) S x (1-x)" dx
:
b) {(x-5)4dx c) (sinto usodo
(⑧a) Use integration by parts to find the integral.
i) Sx cosx dx
EXTRA
(i) Slux.
lux dx.
b). Evaluate the trigonometric integrals:
i) Scos³x sin³x dx
(i). (cos³x dx.
2+2
12+2
E CREDIT. Use trigonometric substitution to solve S√36-72 dx
1+3
3
pts.
13
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