School

Western UniversityDepartment

MathematicsCourse Code

MATH 0110A/BProfessor

Chris BrandlStudy Guide

QuizThis

**preview**shows half of the first page. to view the full**1 pages of the document.**MATH 127 Fall 2012

Practice Assignment (NOT FOR SUBMISSION)

Topics: Integration, area between curves, volumes of revolution

1. Evaluate the following integrals

(a)

Z

4x3−9x2

x4−3x3+ 2

dx

(b)

Z

(3x+ 1)2

3x3dx

(c)

Ze

1

p

ln (x2)+1

x

dx

(d)

Zπ

4

−π

4

x

cos2(x)

dx

2. Find the area of the indicated region.

(a) The region in the ﬁrst quadrant bounded above by y=x2and y=−3x+ 4 and

bounded below by the x-axis.

(b) The region bounded below by y=ex, bounded above by y= 4e−x, and x≥0.

(c) The region bounded by y=x2and y= 2 −x2.

3. Find the volume of the object formed by:

(a) Revolving the region in the ﬁrst quadrant bounded by y=exand its tangent line

at x= 1 about the x-axis.

(b) Revolving the region between x= 0 and x= 3 bounded above by y=

√

x+ 1

and below by y= 1 about the y-axis.

(c) Revolving the region in the ﬁrst quadrant bounded by y= 4−xand the coordinate

axes about the x-axis.

(d) Revolving the region in the ﬁrst quadrant bounded by y= ln xand y= 2 about

the y-axis.

(e) Revolving the region bounded by y= 1 −x2and y= 0 about the line y=−1.

1

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