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Calculus II Quiz Solutions Spring 2008, Quizzes of Calculus

The solutions to a calculus ii quiz taken in spring 2008. The quiz covered topics such as improper integrals, finding areas between graphs, and solving equations for points of intersection. No notes, calculators, books, or cell phones were allowed during the quiz, which lasted for 10 minutes.

Typology: Quizzes

Pre 2010

Uploaded on 08/03/2009

koofers-user-7su
koofers-user-7su 🇺🇸

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(Quiz V-Solution) Calculus II
Spring 2008
Use of notes, calculator, books is not allowed. Make sure that your cell
phone is off. You have 10 minutes for this quiz.
1. Find the improper integral Z
1
1
x3dx
= lim
t→∞ 1
2x2t
1
= lim
t→∞
1
2t2+1
2=1
2
2. Find the area between the graph of y=x2and y=x
Area = Z1
0
(xx2)dx =x2
2
x3
31
0
=1
6sq. units
3. Find the points of intersection of graphs of x=y2and x+y= 1
Solve y2=y+ 1 by using quadratic formula to find the points of
intersection.
1

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(Quiz V-Solution) Calculus II Spring 2008

Use of notes, calculator, books is not allowed. Make sure that your cell phone is off. You have 10 minutes for this quiz.

  1. Find the improper integral

1

x^3 dx

= lim t→∞

[

2 x^2

]t

1

= lim t→∞

2 t^2

  1. Find the area between the graph of y = x^2 and y = x

Area =

0

(x − x^2 )dx =

[

x^2 2 − x

3 3

] 1

0

=^1

sq. units

  1. Find the points of intersection of graphs of x = y^2 and x + y = 1

Solve y^2 = −y + 1 by using quadratic formula to find the points of intersection.

1