Download Math Test Instructions and Problems and more Exams Mathematics in PDF only on Docsity!
MATH 141: TEST 3
Name
Instructions and Point Values: Put your name in the space provided ab ove. Check that your test has exactly 6 di erent pages including one blank page. Work each problem b elow and show ALL of your work. You do not need to simplify your answers. Do NOT use a calculator.
Problem (1) is worth 12 p oints. Problem (2) is worth 20 p oints. Problem (3) is worth 12 p oints. Problem (4) is worth 14 p oints. Problem (5) is worth 14 p oints. Problem (6) is worth 14 p oints. Problem (7) is worth 14 p oints.
(1) Given that
Z 3
0
f (x) dx = 1,
Z 4
0
f (x) dx = 6, and
Z 4
1
f (x) dx = 2, calculate
Z 3
1
f (x) dx.
(2) Calculate each of the following integrals.
(a)
Z = 2
0
sin cos d
(b)
Z
(t + 1)^2 t
t
dt
(c)
Z
p
x + 1 dx
(d)
Z
x
p
x + 1 dx
(5) Calculate the area of the region b ounded by the graphs of x = y 2 y and x = y y 2.
(6) The region in the rst quadrant b ounded ab ove by the ellipse x^2 + 2 y 2 = 9 and b elow by the line y = 2 x revolves ab out the x axis to form a solid. Calculate the volume of the solid.
(7) Calculate the integral
Z b
a
f (x) dx b oxed b elow in the following way. Divide the inter-
val [a; b] into n equal subintervals, calculate the area of the corresp onding circumscrib ed
p olygon, and then let n! 1. You should make use of the formula
X^ n
k =
k =
n(n + 1) 2
:
Your nal answer should b e a numb er.
Z 3
1
(3x 1) dx
