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Bucknell Univ. Math 202 Group Assignment 1 (Calc 11) - Autumn '07 - Prof. Peter Brooksbank, Assignments of Calculus

Bucknell UniversityCalculus
Prof. Peter Brooksbank

A group assignment sheet for math 202 (calculus 11) students at bucknell university during the autumn semester, 2007. The assignment includes three problems that require the application of calculus concepts such as equal areas, integration techniques, and definite integrals.

Typology: Assignments

Pre 2010

Uploaded on 08/18/2009

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koofers-user-m7s 🇺🇸

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Department of Mathematics
Bucknell University
Group Assignment Sheet 1
Autumn Semester, 2007
Math 202 (Calculus
11)
Due:
8-31-2007
Prepared by:
Other Group Members:
(1
Problem
1
1
I
[Equal Areas]
Sketched below are four regions. Determine, with reason, which of these regions have equal area.
(
"My calculator told me"
doesn't constitute a good reason: if you believe two areas to be equal, you
should show that they
exactly
equal.)
pf3

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Department of Mathematics Bucknell University G r o u p Assignment Sheet 1

Autumn Semester, 2007

Math 202 (Calculus 11)

Due: 8-31-

Prepared by:

Other Group Members:

( 1 P r o b l e m 1 1 I [Equal Areas]

Sketched below are four regions. Determine, with reason, which of these regions have equal area.

( "My calculator told me" doesn't constitute a good reason: if you believe two areas t o be equal, you

should show that they exactly equal.)

/ ( Problem 2 1 [More Than One Way]

In an example from class we used integration by parts t o compute the indefinite integral 1 cos2 B dB.

Find an alternative solution that makes use of the trigonometric identity

cos(28) = 2 cos2 0 - 1.

Make sure your answer is the same as the one from class.

/ /Problem1 1 [integration techniques in the abstract]

(a) Suppose you know that J: f (t) dt = a , where a is a constant. Calculate each of the following definite integrals:

(b) Let f be a twice differentiable function such that f (0) = 6, f (1) = 5 and f l ( l ) = 2. Evaluate the

definite integral f i x f1/(x) dx