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Material Type: Exam; Class: CALCULUS II; Subject: Mathematics; University: Clark University; Term: Spring 2004;
Typology: Exams
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Test #1 Name: Section 1 2 3 Instructor:
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 + sec^2 (x) dx
b.
∫ (^) x 2 √ 3 − x^3
dx
c.
sin(t) cos^4 (t) dt
d.
0
3 t (t^2 + 1)^2 dt
e.
∫ (^) π
0
x^2 − π^2 dx
2
x^3 sin(3x)
[10 pts] x + 1 dx
into an integral with respect to u. [Do not evaluate the integral.]
[10 pts] 4. Let f (x) = 2 − | 1 − x|. Let P be the partition
P =
6
° ° ° ° ° ° ° °
°°
@ @ @ @ @ @ @ @ @ @ @
@@
y
x
a. On the graph of f (x) above, draw the rectangles corresponding to Uf (P ).
b. If Q =
, Is Uf (Q) greater than or less than Uf (P )? Why?
c. If R = {− 1 , 0 , 1 , 2 , 3 , 4 }, which is the smallest, Uf (P ), Uf (Q), Uf (R), or
− 1
f (x) dx? Why?
d. Determine for which x values F (x) is concave up, and for which it is concave down.
e. Circle the graph of F (x) among the choices below.
a)
6
y
b)
6
y HH HH HH HH HH HH HH HH
c)
6
y
d)
6
y
