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MATH 101 Webwork 3 Homework Questions and Answers PDF from 2020

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Course
MATH 101 (MATH101)

Institution
University Of British Columbia (UBC )

This is a pdf copy of the Webwork 3 assignment for MATH 101 at UBC with questions and answers. Note that the exact numbers in your question might differ but the answer key here will provide insight for you to tackle the problems nonetheless.

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Uploaded on May 25, 2020
Number of pages 3
Written in 2019/2020
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math 101 differential and integral calculus
math 101 webwork 3 questions and answers pdf
integration by substitution

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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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