MATH 101 Webwork 3 Homework Questions and Answers PDF from 2020

Nikita Sharma 2019W2 MATH 101 209
Assignment Homework 3 due 9/12/14 at 9pm




1. (1 point) Evaluate the following indefinite integral using 4. (1 point)
the substitution u = 3x − 10. Evaluate the indefinite integral

Note: Any arbitrary constants used must be an upper-case ”C”. Z
−2 cos(π/x)
dx
Z
10 x2
dx =
(3x − 10)3 Note: Any arbitrary constants used must be an upper-case
Solution: If u = 3x − 10 then du = 3 dx, or dx = 31 du, and ”C”.
so
10 10
Z Z Z
Correct Answers:
3
dx = du = 10
3 u−3 du.
(3x − 10) 3u3
• -1*-2/pi*sin(pi/x)+C+c
Integrating now gives
Z
10
u−3 du = 10
− 12 u−2 +C = − 35 u−2 +C. 5. (1 point)


3 3 Z 2 p
(x + 8) 4 − x2 dx =
Therefore, −2


10
Z
3
dx = − 35 (3x − 10)−2 +C. Hint 1
(3x − 10)
Hint 2
Correct Answers:
Hint 3
• -(5/3)*(3*x-10)ˆ(-2)+C Correct Answers:

• 2*8*pi
2. (1 point)
Evaluate the indefinite integral
Z 30
Z √
ex 9 + ex dx 6. (1 point) If f is continuous and f (x) dx = 40, find
Z 5 0

Note: Any arbitrary constants used must be an upper-case f (6x) dx.
0
”C”. Answer:
Correct Answers:
Correct Answers:
• 1/6*40
• 2/3*(9+exp(x))ˆ(3/2)+C+c


3. (1 point) 7. (1 point)
Evaluate the indefinite integral Let a be a positive real number. Evaluate the definite integral
Z a
−4(ln(x))2
Z p
dx 8x x2 + a2 dx
x 0

Note: Any arbitrary constants used must be an upper-case in terms of a.
”C”.
Correct Answers:
Correct Answers:
• 1/3*(2*sqrt(2)-1)*aˆ3*8
• -4/3*(ln(x))ˆ3+C+c


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