Assignment 10 Solutions.pdf
Course CodeMATH 0110A/B
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MATH 127 Fall 2012
Practice Assignment (NOT FOR SUBMISSION)
Topics: Integration, area between curves, volumes of revolution
1. Evaluate the following integrals
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=
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
(e) Revolving the region bounded by y= 1 −x2and y= 0 about the line y=−1.
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