September 27, 2007
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Transcript of September 27, 2007
September 27, 2007
Welcome to the cavernous pit of math!
Quiz 2 ReviewQuiz 2 Review
JEOPARDY
Sub-a-Dub-Dub
Par-tay
Revolution of the
Working Classes
Potpourri
100 100 100 100200 200 200 200300 300 300 300400 400 400 400500 500 500 500
Sub-a-Dub-Dub (100)
€
dx
x ln x∫
Sub-a-Dub-Dub (200)
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(1+ x )9
xdx∫
DAILY DOUBLE
Sub-a-Dub-Dub (300)
€
sin3 θ dθ∫
Sub-a-Dub-Dub (400)
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1
25 + x 2dx∫
Sub-a-Dub-Dub (500)
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tan y sec3 y∫ dy
Par-tay (100)
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(x + 2) e2x +1 dx∫
Par-tay (200)
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arctan(1/ x)dx∫
Par-tay (300)
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x 2 sin x dx∫
Par-tay (400)
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arcsin x dx∫
Par-tay (500)
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e x dx∫
Revolution of the Working Classes (100)
Find an integral equal to the volume formed by rotating the area in the first quadrant under x + y = 1 around the line x = -2.
Revolution of the Working Classes (200)
Find the amount of work needed to pulla 5 lb bucket up a 50 ft well.
Revolution of the Working Classes (300)
Write an integral equal to the volume of the solid formed by rotating the area under y = sin x for 0 ≤ x ≤ around the y-axis.
Revolution of the Working Classes (400)
Express the volume formed by rotating the area between y = x2 and y = x3 around the y-axis as an integral.
DAILY DOUBLE
Revolution of the Working Classes (500)
Set up an integral equal to the amount of work needed to pump all the water out of a tank that is a circular cylinder with base radius 3 ft and height 8 ft, if the tank is half full of water. (Water weighs 62.5 lb/ft2.)
Potpourri (100)
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x + 2x 2
xdx∫
Potpourri (200)
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cos x dx∫
Potpourri (300)
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x
x 2 −16dx∫
Potpourri (400)
If
then find an expression for tan in terms of x.
€
x = 3sinθ
Potpourri (500)
€
e−x 2
sin x dx−1
1
∫