AP Calculus AB
Home Enjoyment Ch. 7A – Area, Volumes, Arc Lengths
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Date
Period
Objective
Home Enjoyment
2/10/2017
2/13/2017
2/14/2017
2/15/2017
2/16/2017
2/17/2017
Friday
Monday
Tuesday
Wednesday
Thursday
Friday
Area Between Curves
Volume by Cross Sections
Volume by Disk and Washers
Volume by Shells
Arc Length, Surface Area
8th grade visit, Leg
2/20/2017
2/21/2017
Monday
Tuesday
Hershey Kiss Lab
Test
Ch. 7A HW #1 and CTJ
Problem Set Due, Ch. 7A HW #2
Ch. 7A HW #3
Ch. 7A HW #4
Ch. 7A HW #5 - Study for Formula Quiz
Formula Quiz, work on HW #6 in class
Problem Set Due
Ch. 7A HW #7, Study for Test
Test Ch. 7A, LBB and HW due
All Calculator Test with some Noncalculator required: In your homework notebook, you must
sketch all graphs with a sample rectangle and set up the integral you put in your calculator,
then answer.
#1
Finding Area between Curves and Integration as Accumulation:
p. 442 (Sec. 7.1) #3, 5, 7, 11, 13, 19, 21, 27, 39, 59a, 61, 71 , 83-85 all (explain both T & F)
p. AP7 #2 (Noncalculator), 4ab (Noncalculator)
(A) Oil is leaking from a tanker at the rate of R(t) = 2000e-0.2t gallons per hour, where t is
measured in hours. How much oil leaked out of the tanker after 10 hours?
19 pts.
(Calculator problem) (Ans: 8646 gal.)
Critical Thinking Journal (CTJ 15 pts.) p. 442 #65, 66, 68 (Graph and draw rectangles
and explain using accumulation discussion.)
#2
Finding Volume of a Solid by Cross Sections
p. 453 (Sec. 7.2) #71 ab, 72abcd. p. AP7 #1 (calculator), 3abc (Noncalculator)
14 pts.
3
(A) The base of the solid is bounded by y = x , y = 0, and x = 1. Find the volume of the solid
for each of the following cross sections (taken perpendicular to the y=axis):
(a) Squares, (b) semicircles, (c) equilateral triangles, (d) Rectangles whose heights are
twice the length of the bases. (Answers on Moodle.)
#3
Finding Volume of a Solid of Revolution by Disk and Washer Method:
p. 453 (Sec. 7.2) #3, 5, 7, 9, 11abcd, 13ab, 21, 33, 55, (Make sure to sketch all the graphs with a
rectangle and three dimensional slice formed by revolving that rectangle about the axis of revolution.) 22 pts.
p. AP7 (Set up integrals for #5 and 6, do not evaluate) #5abc (Noncalculator), 6abc, (Noncalculator),
(A) Calculator allowed but you have to show setup. (Ans: on Moodle)
(Set up integrals, do not evaluate)
AP Calculus AB Ch. 7A HW – Area, Volumes, Arc Lengths
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#4
Finding Volume of a Solid of Revolution by the Shell Method
p. 462 (Sec. 7.3) #3, 5, 7, 9, 15, 25, 29abc,
p. AP7 (Set up integrals for #9 and 10, do not evaluate) #9abc, 10abc
(A) y = 2e-x, y = 0, x = 0, Approximate the answer for the volume revolving the region about
the y-axis. Do not calculate: (a) ½ (b) -2, (c) 4 (d) 7.5, (e) 15 (Ans: (d))
16 pts.
#5
Quiz on all formulas and simple problems for disk, washer, and shell. (no calculator)
(If you are at leg or involved in 8th grade visit, come in before school on Monday to make up
this quiz.)
#6
Finding Arc Lengths and Surface Area
p. 474 (Sec. 7.4) #3, 15, 21abc, 23abc, 37, 39, 43, 47, 48,
p. AP7 (Set up integrals and evaluate on calculator), #7abc, 8abc
(A) Work problem below; calculator allowed but you have to show setup.
(Ans: on Moodle.)
#7 Test tomorrow. Hand in LBB and Homework Notebook.
23 pts.
AP Calculus AB Ch. 7A HW – Area, Volumes, Arc Lengths
Little Black Book of Calculus Properties
Ch. 7A – Area, Volume and Arc Length
7A-1
7A-2
7A-3
Geometry Formulas for Area, Volume, and Surface Area (areas of square,
rectangle, circle, semicircle, annulus, triangle, equilateral triangle, Hero’s formula
for finding area; volumes of rectangular solid, cube, sphere, cone, pyramid, prism,
cylinder, ellipsoid, surface areas of cylinder, prism, cone, sphere)
Integration as Accumulation (discuss the meaning of integration as
accumulation, give a real world word problem example)
Area Between Curves (formula, 5 step process, how to slice – draw sample
rectangle, ex. solve problem drawing graph, rectangle, and setting up integral – you
do not have to solve)
FOLDABLE
7A-4 Volume of Solid with Known Cross Section (formula, how to draw
and slice, ex. using equilateral triangles, sketching the graph, slicing and
setting up the integral)
7A-5 Volume of Solid of Revolution by Disks (formula, how to slice, ex.
graphing, slicing and setting up integral to revolve around x axis and y
axis, and line x = k)
7A-6 Volume of Solid of Revolution by Washer (formula, how to slice,
ex. graphing, slicing and setting up integral to revolve around x axis and
y axis, and line x = k)
7A-7 Volume of Solid of Revolution by Shell (formula, how to slice, ex.
7A-8
7A-9
graphing, slicing and setting up integral to revolve around x axis and y
axis, when to use shell, disk, or washer)
Length of Arc (formula, when to use dx and dy, ex. each)
Surface Area of Solid of Revolution (formula, when to use dx and dy, ex each)
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