Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
A math exam focusing on integration and surface area calculations. The exam consists of 12 multiple choice questions and 3 free response questions. No calculators are allowed, and one piece of paper is permitted for writing. There is no penalty for guessing and no partial credit for multiple choice questions. Questions include evaluating integrals and finding surface areas generated by revolving curves about axes.
Typology: Exams
1 / 17
This page cannot be seen from the preview
Don't miss anything!
Math 104 Practice Midterm Exam 2B
Name
Write all answers (A, B, C, D, E, F) in the spaces provided below!
1 − x^2 with 0 ≤ x ≤ 1 / 2 about the x-axis.
A.) 2π
B.) π
C.) 43 π
D.)
√ 3 4 π
E.) 1
F.) (^43)
∫ (^1)
0
x ln x dx
F.) The integral diverges
0
sin^3 (x) dx
F.) The integral diverges
0
(x − 2)(x − 3)
dx
A.) ln 12 B.) ln 23 C.) ln 34 D.) ln 43 E.) ln 32 F.) ln 2
1
x^2 ln x dx
A.) 0 B.) 1 C.) ln 2 − 1 D.) 29 e^2 + 19 E.) 29 e^2 + 13 F.) 13 e^2 − 1
2
x^2 (x − 1)
dx
A.) 1 B.) 94 C.) ln 3 D.) 4 ln 2 − 1 E.) 4 ln 2 − 3 ln 3 F.) 2 ln 2 − ln 3 − (^16)
0
(9 + x^2 )^3 /^2
dx
A.) 143 B.) 23 ln 3 C.) 43 π D.) 4. 75 E.) 4/ 45 F.) 1
0
(x − 1)^3
dx
A.) 38 B.) 12 ln 3 C.) 94 π D.) 0 E.) 83 F.) The integral diverges.
Free Response 2. Evaluate the integral
∫ (^) π
0
sin^4 (x) dx
Free Response 3. Suppose p(x) is the demand curve for a product (i.e. p(x) is price in dollars at which x units can be sold). Then the consumer surplus for a price P is
0
p(x) − P
(where p(A) = P ).
Suppose Widget International just invented a new Super Widget such that the demand curve for super widgets is given by
p(x) = 64 · (2−x) where p(x) is in $
What is the consumer surplus at a price of $16?
