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)

€

(1+ x )9

xdx∫

DAILY DOUBLE

Sub-a-Dub-Dub (300)

€

sin3 θ dθ∫

Sub-a-Dub-Dub (400)

€

1

25 + x 2dx∫

Sub-a-Dub-Dub (500)

€

tan y sec3 y∫ dy

Par-tay (100)

€

(x + 2) e2x +1 dx∫

Par-tay (200)

€

arctan(1/ x)dx∫

Par-tay (300)

€

x 2 sin x dx∫

Par-tay (400)

€

arcsin x dx∫

Par-tay (500)

€

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)

€

x + 2x 2

xdx∫

Potpourri (200)

€

cos x dx∫

Potpourri (300)

€

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

∫