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Material Type: Exam; Professor: Joyce; Class: CALCULUS II; Subject: Mathematics; University: Clark University; Term: Spring 2005;
Typology: Exams
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Test #1 Name: (print neatly) Instructor: (sign)
This exam is CLOSED NOTES and CLOSED BOOK. There are NO CALCULATORS allowed. To get full credit you must show all work neatly in the space provided on the test paper.
a.
∫ 5 x^2 − 3 +
x +
x
dx
b.
∫ x^2 sin(3 − x^3 ) dx
c.
∫ sin(t)(cos^2 (t) + 1) dt
d.
∫ (^2) 0
x −
2 dx
e.
∫ (^2) 1
t − t−^1 t^4
dt
f.
∫ sec^2 (θ + π) dθ
P =
{ − 1 , −
} .
6
° ° ° ° ° °
°°
J J J J J J J J J J J
y
x
a. On the graph of f (x) above, draw the rectangles corresponding to Lf (P ).
b. Suppose Q = {− 1 , 0 , 1 , 2 , 4 }, What is Uf (Q)?
c. Order the following numbers from smallest to largest: Uf (Q), Lf (Q), Uf (P ), Lf (P ), and
∫ (^4)
− 1
f (x) dx.
a. Show that it must be true that
∫ (^2)
1
3 + f (x) + 2[f (x)]^2 dx < 30.
b. Give an example of to show that it may be true that
∫ (^2)
1
3 + f (x) + 2[f (x)]^2 dx > 10.
