Math 152 (21-23): Workshop 1
September 11, 2015
1-1. Sketch the region R defined by 1 x 2 and 0 y 1/x3 .
a) Find (exactly) the number a such that the line x = a divides R into two parts of equal area.
b) Then find (to 3 places) the number b such that the
Volumes
A. Consider the region bounded by the graphs of
and
Find the volume of the solid obtained by rotating the above region about the following axes. Find
the volume twice each time: first using the cross-sections method and then again using the shells
Final Exam Review Questions Part 1.
Area between curves- Volumes- Average Value-integration by parts-improper integral- parametric-polardifferential equation
1. The base of a solid is the region inside the ellipse
Each cross section of the
solid perpendic
MATH 152 REVIEW
Area between curves: Find intersection point (unless a, b given), find top function f(x), bottom function g(x)
function is with respect to y, find right function f(y), and left function g(y)
Example:
Volume by cross section
(OR if
Volume o
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2/4/2015
TECHNIQUES OF INTEGRATION
Due to the Fundamental Theorem of Calculus
7
(FTC), we can integrate a function if we know
an antiderivative, that is, an indefinite integral.
TECHNIQUES OF INTEGRATION
We summarize the most important integrals
we have