PURITY WANGECI MWANGI
Assignment Homework 1 due 03/05/2020 at 11:59pm EAT
SMA104S Calculus II
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•
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1. (1 point)
Use the figure below, which shows the graph of y = f (x), to
answer the following questions.
(incorrect)
4. (1 point)
Z 18
f (x) dx −
Z 9
5
where a =
Z b
f (x) dx =
5
and b =
f (x) dx
a
.
Answer(s) submitted:
•
•
(incorrect)
5. (1 point)
R √
Given that 49 9 x dx =
(Click on the graph to get a larger version.)
R3
A. Estimate the integral: −3
f (x) dx ≈
(You will certainly want to use an enlarged version of the graph
to obtain your estimate.)
B. Which of the following average values of f is larger?
342
3 ,
what is
R4 √
9
9 t dt ?
Answer(s) submitted:
•
(incorrect)
6. (1 point)
• A. Between x = −3 and x = 3
• B. Between x = 0 and x = 3
Z 1
Evaluate
−10x2 cos(x) dx.
1
Answer(s) submitted:
•
•
Answer(s) submitted:
(incorrect)
(incorrect)
•
2. (1 point)
R
If 14 (3 f (x) + 5) dx = 17, then
R4
1 f (x)dx =
7. (1 point)
Let
Z 2
Answer(s) submitted:
•
f (x) dx = −10,
Z 3
0
Z 2
f (x) dx = 8,
0
Z 3
g(x) dx = 8,
0
Use these values to evaluate the given definite integrals.
(incorrect)
Z 2
( f (x) + g(x)) dx =
a)
3. (1 point)
R
Let 04 f (x) dx = 7.
(a) What is the average value of f (x) on the interval from
x = 0 to x = 4?
average value =
(b) If f (x) is even, find each of the following:
R4
−4 f (x) dx =
the average of f (x) on the interval x = −4 to x = 4 =
(c) If f (x) is odd, find each of the following:
R4
−4 f (x) dx =
the average of f (x) on the interval x = −4 to x = 4 =
Z0 3
b)
( f (x) − g(x)) dx =
Z 03
(3 f (x) + 2g(x)) dx =
c)
2
d) Find the value a such that
a=
Answer(s) submitted:
•
•
•
•
Answer(s) submitted:
•
•
(incorrect)
1
Z 3
(a f (x) + g(x)) dx = 0.
0
2
g(x) dx = −14
Answer(s) submitted:
•
8. (1 point)
Find area of the region under the curve y = 2x3 − 7 and above
the x-axis, for 4 ≤ x ≤ 9.
area =
(incorrect)
10. (1 point)
Evaluate the definite integral:
Answer(s) submitted:
•
Z 17
dx =
(incorrect)
6
9. (1 point) Evaluate the definite integral
Z 8
Answer(s) submitted:
•
(64 − x2 )dx
−8
(incorrect)
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