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
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
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 th
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
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
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 +
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 .
Hin