Class Notes (839,195)
Canada (511,223)
Mathematics (442)
MA104 (18)


2 Pages

Course Code
Olivia Ozlem Mesta

This preview shows 80% of the first page. Sign up to view the full 2 pages of the document.
MA104 – Midterm Test February 10, 2012 Page 1 of 2 1. Evaluate each of the following integrals. Show all of your work. Rπ/2 [4 marks] (a) cos (x)sin (x)dx R0 [2 marks] (b) π/4 tan (t)dt R0 √ x [3 marks] (c) x−4 dx Rπ/4 [3 marks] (d) |1 − sec(x)|dx −π/4 Rln2 [2 marks] (e) 0 sinh(x)dx [5 marks] 2. Give the Riemann sum argument, using regular partitions, to derive the formula for volumes of revolution. Assume the area under y = f(x) (where f is a continuous function), above the x-axis, between x = a and x = b (b > a) is rotated about the x-axis. Make sure all terms are defined. √ [5 marks] 3. Determine the exact value of the length of the arc traversed (coverey =by 1 − x 2 from p the point (0,1) to (1/2, 3/4). [6 marks] 4. Determine the lateral surface area generated by rotating the ay = f(x) = ln(1 − x ) 2 , from x = 0 to x = 1/2, about the y-axis. (Note: The problem is changed from the original one) [5 marks] 5. Suppose that the function y = f(x), 4 ≤ x ≤ 6, is twice continuously differentiable on [4,6] and |f (x)| ≤ 3 on [4,6]. Determine the number n of subdivisions necessary using the R6 trapezoid rule to ensure the error in approximatin4 f(x)dx is less than 0.01. 6. Compute each of the following integrals, using the method of improper integration. The majority of marks in each will be for proper form. R∞ −x [4 marks] (a) 0 xe dx R1 −1/2 2 [4 marks] (b) 0 x (1 − x) dx [4 marks] 7. Use the information in the given table about the function y = f(x), 1 ≤ x ≤ 2 and Simp-
More Less
Unlock Document

Only 80% of the first page are available for preview. Some parts have been intentionally blurred.

Unlock Document
You're Reading a Preview

Unlock to view full version

Unlock Document

Log In


Join OneClass

Access over 10 million pages of study
documents for 1.3 million courses.

Sign up

Join to view


By registering, I agree to the Terms and Privacy Policies
Already have an account?
Just a few more details

So we can recommend you notes for your school.

Reset Password

Please enter below the email address you registered with and we will send you a link to reset your password.

Add your courses

Get notes from the top students in your class.