MATH 181, Exam I (10) 1. a) Write down a denite integral that gives the length of the curve y = sin(2x) as x ranges from 0 to . Do not compute the integral. b) Write down a denite integral that gives the surface area of the surface obtained by revolving t
MATH 181
Practice Problems
1. Determine the equation of the tangent line to the curve given parametrically by
x(t) = t sin t and y (t) = 1 cos t, 0 t 2 , at t = 0. Find the length of this
curve from t = 0 to t = 2 . Hint: 2 2 cos t = 4 sin2 (t/2)
dy
1
2.
MATH 181, Exam I (20) 1. Compute (20) 2. Suppose F (x) =
0 2
a)
0
x2 dx x3 + 1
x
2
and
b)
x5
x3 + 1 dx.
et dt
for x > 0.
x ? x F (x) (20) 3. Fill in the blank of the punch line of these two famous theorems. Compute F (x). What is lim a) Suppose f is cont
MATH 181, Exam II
(30) 1. Compute the following integrals. a) b) c) sin2 (2x) dx x2 2x 3 dx + 2x + 5
xe2x dx x3 dx. 9 x2
(20) 2. Use the method of Trigonometric Substitution to compute (20) 3. Compute
n
lim
3 1 n
n
.
(10) 4. For what values of p does the
MATH 181
Exam I
October 4, 2011
Closed book and notes. No calculators.
(20) 1. Evaluate lim
x0
(20) 2. Find
3x sin 3x
.
x3
x2 (x + 1)3/2 dx. (Dont forget the plus . . . )
(20) 3. Graph the functions y = x3 and y = x4 on the interval 0 x 1. (Note that
x4 <
MATH 181 Exam 2
(20) 1. Compute the following integrals.
a)
cos3 x sin2 x dx
b)
x3 ln x dx
c)
x2
dx
4 x2
(20) 2. a) Write down the FORM of the partial fraction decomposition for
x6 + ex4 + x3 + 2x2 + 1000
.
x2 (x 1)3 (x2 + 2x + 2)
Do NOT compute the coeci
Exam Q {/LZS.
WM m
i) 8 Cog? 63/26 M
: i g @535 f/X ((05?!
W
(mm 4 (gm)
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MATH 181, Final Exam
x
(25) 1. Dierentiate
x
(t + 1)2
dt with respect to x.
1 + t5
(50) 2. Compute the following integrals.
a)
x3
dx
(1 + x2 )1/3
b)
1
dx
(1 + x2 )2
c)
d)
e)
Hint: let u = 1 + x2 .
Hint: let x = tan .
x2 ln x dx
x2
x2
dx
4x + 8
xe2x dx
n
Exam Q {/LZS.
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i) 8 Cog? 63/26 M
: i g @535 f/X ((05?!
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(mm 4 (gm)
This pencast was created with my Livescribew smartpen. Click here to see how to create your own. I x xi y