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7 Practice Problems for Calculus II - Past Test 1 | MATH 121, Exams of Calculus

Material Type: Exam; Class: CALCULUS II; Subject: Mathematics; University: Clark University; Term: Spring 2004;

Typology: Exams

Pre 2010

Uploaded on 08/07/2009

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Math 121 Calculus II Spring 2004
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.
1. Compute the following integrals: [9 pts each]
a. Z5x23 + sec2(x)dx
b. Zx2
3x3dx
c. Zsin(t) cos4(t)dt
pf3
pf4
pf5

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Math 121 Calculus II Spring 2004

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.

  1. Compute the following integrals: [9 pts each]

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

  1. Use the substitution u = 3x to transform the integral

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 =

− 1 , −^1

6

° ° ° ° ° ° ° °

°°

@ @ @ @ @ @ @ @ @ @ @

@@

y

x

a. On the graph of f (x) above, draw the rectangles corresponding to Uf (P ).

b. If Q =

− 1 , −^1

, 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?

  1. Suppose that the acceleration of a particle along the x axis is given [10 pts] a(t) = 2t − 10 for 0 ≤ t ≤ 5, and suppose that at t = 5 the particle is at rest at the origin, that is, x(5) = 0 and v(5) = 0. What is the position of the particle at t = 0?

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

-1 1 x

y

b)

6

-1 1 x

y HH HH HH HH HH HH HH HH

c)

6

-1 1 x

y

d)

6

-1 1 x

y