8:24 Back Exercise 2 on Properties of Definite Integral... 19 1 of 1 201-NYB Calculus II Properties of Definite Integrals, Antiderivatives and Infinite Integrals 1. Suppose that f and g are integrable and f(x)dx = -4, f(x)dx=2, 9(x)dr=3 and 9(x)dr =-1. Find (b) f(x)dx (c)(t)dt (d)3f(x)-49(x)]dx (e) 9(x)dx (1) f(x)+9(x)]dx 2. Graph the integrands and use known area formulas to evaluate the definite integrals: (a)x-1dx (b) 3r dr, a > 0 2+3 (c) f(x)dz where f(x)= -452<-2 -25252 is a piece-wised defined function. 3. Use the Max-Min Inequality to find upper and lower bounds for the value of the following definite integrals: (a) 1+2 dx (b)(x-2 sin x) dr 4. Find an anti-derivative for each function. (Note: You may check your answer by differentiation.) (a)(x-3)²+5x-7 2 csc cote (b) e² + (c) 3 sin 6+ 2 (d) 2-tan² t 1 (e) (S) 49x²+9 5. Find the following indefinite integrals: (a) / [x²(5x²-2 1 -2r)- dr 22 (d)/3 24. +9x²-4x+6 dr (e) 2 de 7 (6)√√+3 2-cos 0 dt (c) secr(sec.r-tan x) dr ()sinz dz 6. A car moves on a straight road with acceleration a(t) = 3sint 2 cost m/s², subject to the conditions (0) = 2m/s and s(0) = 0m. Find the formulas for the velocity v(t) and the position s(t) of the car in terms of t. d's dt2
8:24 Back Exercise 2 on Properties of Definite Integral... 19 1 of 1 201-NYB Calculus II Properties of Definite Integrals, Antiderivatives and Infinite Integrals 1. Suppose that f and g are integrable and f(x)dx = -4, f(x)dx=2, 9(x)dr=3 and 9(x)dr =-1. Find (b) f(x)dx (c)(t)dt (d)3f(x)-49(x)]dx (e) 9(x)dx (1) f(x)+9(x)]dx 2. Graph the integrands and use known area formulas to evaluate the definite integrals: (a)x-1dx (b) 3r dr, a > 0 2+3 (c) f(x)dz where f(x)= -452<-2 -25252 is a piece-wised defined function. 3. Use the Max-Min Inequality to find upper and lower bounds for the value of the following definite integrals: (a) 1+2 dx (b)(x-2 sin x) dr 4. Find an anti-derivative for each function. (Note: You may check your answer by differentiation.) (a)(x-3)²+5x-7 2 csc cote (b) e² + (c) 3 sin 6+ 2 (d) 2-tan² t 1 (e) (S) 49x²+9 5. Find the following indefinite integrals: (a) / [x²(5x²-2 1 -2r)- dr 22 (d)/3 24. +9x²-4x+6 dr (e) 2 de 7 (6)√√+3 2-cos 0 dt (c) secr(sec.r-tan x) dr ()sinz dz 6. A car moves on a straight road with acceleration a(t) = 3sint 2 cost m/s², subject to the conditions (0) = 2m/s and s(0) = 0m. Find the formulas for the velocity v(t) and the position s(t) of the car in terms of t. d's dt2
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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![8:24
Back Exercise 2 on Properties of Definite Integral...
19
1 of 1
201-NYB Calculus II
Properties of Definite Integrals, Antiderivatives and Infinite Integrals
1. Suppose that f and g are integrable and f(x)dx = -4, f(x)dx=2, 9(x)dr=3 and
9(x)dr =-1. Find
(b) f(x)dx (c)(t)dt
(d)3f(x)-49(x)]dx (e) 9(x)dx (1) f(x)+9(x)]dx
2. Graph the integrands and use known area formulas to evaluate the definite integrals:
(a)x-1dx
(b) 3r dr, a > 0
2+3
(c) f(x)dz where f(x)=
-452<-2
-25252
is a piece-wised defined function.
3. Use the Max-Min Inequality to find upper and lower bounds for the value of the following definite
integrals: (a) 1+2 dx
(b)(x-2 sin x) dr
4. Find an anti-derivative for each function. (Note: You may check your answer by differentiation.)
(a)(x-3)²+5x-7
2
csc cote
(b) e² +
(c) 3 sin 6+
2
(d) 2-tan² t
1
(e)
(S)
49x²+9
5. Find the following indefinite integrals:
(a) / [x²(5x²-2
1
-2r)-
dr
22
(d)/3
24.
+9x²-4x+6
dr
(e) 2 de
7
(6)√√+3
2-cos 0
dt (c) secr(sec.r-tan x) dr
()sinz
dz
6. A car moves on a straight road with acceleration a(t) =
3sint 2 cost m/s², subject
to the conditions (0) = 2m/s and s(0) = 0m. Find the formulas for the velocity v(t) and the
position s(t) of the car in terms of t.
d's
dt2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa7634a6a-5ecc-40e2-9892-46ba7a4cefd4%2Fb698acf1-0374-4cb3-819c-bfcb8a8ab832%2Fgiborl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:8:24
Back Exercise 2 on Properties of Definite Integral...
19
1 of 1
201-NYB Calculus II
Properties of Definite Integrals, Antiderivatives and Infinite Integrals
1. Suppose that f and g are integrable and f(x)dx = -4, f(x)dx=2, 9(x)dr=3 and
9(x)dr =-1. Find
(b) f(x)dx (c)(t)dt
(d)3f(x)-49(x)]dx (e) 9(x)dx (1) f(x)+9(x)]dx
2. Graph the integrands and use known area formulas to evaluate the definite integrals:
(a)x-1dx
(b) 3r dr, a > 0
2+3
(c) f(x)dz where f(x)=
-452<-2
-25252
is a piece-wised defined function.
3. Use the Max-Min Inequality to find upper and lower bounds for the value of the following definite
integrals: (a) 1+2 dx
(b)(x-2 sin x) dr
4. Find an anti-derivative for each function. (Note: You may check your answer by differentiation.)
(a)(x-3)²+5x-7
2
csc cote
(b) e² +
(c) 3 sin 6+
2
(d) 2-tan² t
1
(e)
(S)
49x²+9
5. Find the following indefinite integrals:
(a) / [x²(5x²-2
1
-2r)-
dr
22
(d)/3
24.
+9x²-4x+6
dr
(e) 2 de
7
(6)√√+3
2-cos 0
dt (c) secr(sec.r-tan x) dr
()sinz
dz
6. A car moves on a straight road with acceleration a(t) =
3sint 2 cost m/s², subject
to the conditions (0) = 2m/s and s(0) = 0m. Find the formulas for the velocity v(t) and the
position s(t) of the car in terms of t.
d's
dt2
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