Advice and Notes:
-
Review all class notes, notes written on your homework and quizzes, and any appropriate handouts.
-
No calculators are necessary for any exam, so don't use any.
-
Sometimes you'll be asked to set-up but not evaluate an integral.
-
Sometimes you'll be asked to actually evaluate an integral exactly.
-
In all the integration applications below, be able to sketch a typical slice, and its approximation (a rectangle for area, a disk or washer for volume, a line segment for length, and so on)
-
In every integration application also be able to write a formula for that approximated slice, either
,
,
or
,
involving
or
before
writing the final integral
Applications of Integration:
-
Area
between
curves, "Upper - Lower" and "Rightmost - Leftmost"
-
Volume
of
Solids of Revolution, by disks or washers, around various horizontal or
vertical axes of revolution
-
Arc Length
of
a plane curve, in both standard and parametric forms
-
Surface area
of
a Solid of Revolution (of lesser importance than length)
-
The Average Value of a Function on an interval
-
Work
,
springs, Hooke's Law (of lesser importance than pumping fluids)
-
Work
,
pumping fluids (do-it-yourself integrals)
Integration Techniques:
-
Review Calculus I integration background: Integration by Substitution with "translation boxes", and Basic Integrals as reviewed in section 8.1
-
Integration by Parts, with translation boxes, LIATE (or LIPET)
-
Integration of Powers of certain Trigonometric Functions,
or
-
Integration using Trigonometric Substitutions for
,
,
or
,
as well as
