Nikita Sharma 2019W2 MATH 101 209
Assignment Homework 2 due 9/12/14 at 9pm
1. (1 point)R 3. (1 point)
Let g(x) = 0x f (t) dt, where f is the function whose graph is Use the Fundamental Theorem of Calculus to evaluate
Z 1
shown below.
3eu+1 du.
−1
(a) Evaluate g(x) for x = 0, 1, 2, 3, 4, 5, and 6.
g(0) = Correct Answers:
g(1) = • 3*(eˆ2-1)
g(2) =
g(3) = 4. (1 point)
g(4) = Use the Fundamental Theorem of Calculus to evaluate
Z 2
g(5) =
g(6) = −6x(2 + x5 ) dx.
0
(b) Estimate g(7). Correct Answers:
g(7) ≈ • 156/7*-6
(c) At what value of x does g attain its maximum? 5. (1 point)
Z 5π/2
x= Evaluate −3 sin(x) dx.
π/4
(d) At what value of x does g attain its minimum? Correct Answers:
x= • -3/sqrt(2)
Graph of f : Z 3
6. (1 point) Evaluate the integral (2ex + 5 cos x) dx.
0
Answer:
Correct Answers:
• 38.8767
Correct Answers: Z 8
7. (1 point) If f (1) = 16, f 0 is continuous, and f 0 (t) dt =
• 0 1
• 1/2 29, what is the value of f (8)?
• 0 Answer:
• -1/2 Correct Answers:
• 0 • 16+29
• 3/2
8. (1 point) Let g(x) = 0x f (t) dt, where f is the function
R
• 4
• 6.2 whose graph is shown. Answer the following questions only on
• 7 the interval [0, 10].
• 3
2. (1 point)
u3
Z 1
Let y = 2
du. Use the Fundamental Theorem of
1−9x 1 + u
Calculus to find y0 .
y0 =
Correct Answers:
• (-1)*(1-(9)*x)ˆ3/(1+(1-(9)*x)ˆ2)*(-1)*9
1
Assignment Homework 2 due 9/12/14 at 9pm
1. (1 point)R 3. (1 point)
Let g(x) = 0x f (t) dt, where f is the function whose graph is Use the Fundamental Theorem of Calculus to evaluate
Z 1
shown below.
3eu+1 du.
−1
(a) Evaluate g(x) for x = 0, 1, 2, 3, 4, 5, and 6.
g(0) = Correct Answers:
g(1) = • 3*(eˆ2-1)
g(2) =
g(3) = 4. (1 point)
g(4) = Use the Fundamental Theorem of Calculus to evaluate
Z 2
g(5) =
g(6) = −6x(2 + x5 ) dx.
0
(b) Estimate g(7). Correct Answers:
g(7) ≈ • 156/7*-6
(c) At what value of x does g attain its maximum? 5. (1 point)
Z 5π/2
x= Evaluate −3 sin(x) dx.
π/4
(d) At what value of x does g attain its minimum? Correct Answers:
x= • -3/sqrt(2)
Graph of f : Z 3
6. (1 point) Evaluate the integral (2ex + 5 cos x) dx.
0
Answer:
Correct Answers:
• 38.8767
Correct Answers: Z 8
7. (1 point) If f (1) = 16, f 0 is continuous, and f 0 (t) dt =
• 0 1
• 1/2 29, what is the value of f (8)?
• 0 Answer:
• -1/2 Correct Answers:
• 0 • 16+29
• 3/2
8. (1 point) Let g(x) = 0x f (t) dt, where f is the function
R
• 4
• 6.2 whose graph is shown. Answer the following questions only on
• 7 the interval [0, 10].
• 3
2. (1 point)
u3
Z 1
Let y = 2
du. Use the Fundamental Theorem of
1−9x 1 + u
Calculus to find y0 .
y0 =
Correct Answers:
• (-1)*(1-(9)*x)ˆ3/(1+(1-(9)*x)ˆ2)*(-1)*9
1
