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MATH 1510-Calculus 1
Spring 2020-NCC (Kothari)
Week of May 4 (Wk 16)
Quiz 13 (4.9-P2, 5.1, 5.2-P1) Name:
Due: Wed. 5/6, by 5:20 pm on D2L
1. Show all your work. Leave your answers in exact form unless asked to round. Clearly indicate your
final answer by putting a box around it.
2. If you do not have access to a printer, write the solutions clearly in a notebook with the correct
question number. It is not necessary to copy the entire question.
3. If you are using your cell phone to capture pictures, please use Portrait mode and good lighting in the
background without shadows. I do not need to see what is surrounding your paper.
4. Scan all pages into a single pdf file. (You may use the app on your phone or download all pictures on
your computer, then cut and paste them into a word document, save as pdf )
5. Submit the single pdf file by upload it on D2L under Assessment-> Assignment→ Quiz 13 folder.
6. Pages uploaded one by one will not be graded.
#1. For the function 𝑓(𝑥) = 𝑥 5 − 2𝑥 −2 + 1, find the antiderivative 𝐹(𝑥) that satisfies the condition
𝐹(1) = 0
#2. Suppose 𝑓(𝑥) = 𝑥 2 where 0 ≤ 𝑥 ≤ 8 and we use 𝑛 = 32 subintervals of equal lengths.
a) What would be the length of each subinterval?
b) Find the midpoint of the first subinterval.
#3. If the interval [1,9] is partitioned into 4 subintervals of equal length, what is ∆𝑥 ? List the four
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#4. Let 𝑅 be the region bounded by the graph of 𝑓(𝑥) =
cos 𝑥 and the 𝑥 −axis between [0, 2 ].
Approximate the area of 𝑅 using a left end points with 𝑛 = 6 subintervals. (Round your final result to three
#5. Suppose 𝑓(𝑥) = −5. What is the weighted area of the region bounded by the graph of 𝑓 and the
𝑥 −axis on the interval [1,5]. Make a sketch of the function and the region.
#6. Graph 𝑓(𝑥) = 𝑥 and use geometry to evaluate ∫−1 𝑓(𝑥) 𝑑𝑥
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