6.1:
Areas Between Curves
6.2: Volumes Using Washers and Discs
6.3: Shells
6.5:
Average Value of a Function
Potpourri
100
Sketch then find the area. y=e^x, y=x^2-1, x=-1, x=1
e - (1/e) + 10/3
100
Set up the integral for: y=e^-x^2, y=0, x=-1, x=1; about the x-axis. Evaluate the integral to the nearest 3 decimal places.
3.758
100
Set up the integral using the shell method. Evaluate and round to the nearest 3 decimal places. y=xe^-x, y=0, x=2; about the y-axis
4.06300
100
What is the formula used to calculate the average value of a function over a specified interval?
1/(b-a) * integral from a to b of f(x)*dx
100
In finance, what does the letter P stand for in APR?
Percentage
200
Sketch then find the area. y=(x-2)^2, y=x
9/2
200
y = √(x-1) y = 0 x = 5 about the x-axis
8pi
200
Use shells to find the volume given by rotating the region bounded by the curves about the x-axis. xy=1, x=1, y=1, y=3
4pi
200
Why is the f[ave] formula used, instead of the usual mean calculation? (add all values together, divide by number of values).
The formula is precise and accounts for ALL values between the two intervals, whereas the usual mean calculation only takes certain points along the intervals into account.
200
In "Peanuts", what color is Woodstock?
Yellow
300
Sketch then find the area. y=e^x, y=xe^x, x=0
e - 2
300
x = 2√y x = 0 y = 9 about the y-axis
162pi
300
Use shells to find the volume given by rotating the region bounded by the curves about the x-axis. y=x^3, y=8, x=0
768pi/7
300
Set up an equation to find the average value of the function f(x) = x^5ln(8x^2) over the interval [-y, 32y].
(1/33y) * integral from -y to 32y of x^5ln(8x^2)
300
Which American novelist wrote "For Whom the Bell Tolls?"
Ernest Hemingway
400
Sketch then find the area. x=1-y^2, x=y^2-1
8/3
400
y = x^3, y = x, x>0; about the x-axis
4pi/21
400
Use shells to find the volume given by rotating the region bounded by the curves about the x-axis. x=1+(y-2)^2, x=2
16pi/3
400
Find the average value of the function y = sin(x)cos(x)dx over the interval [pi/2, pi].
-1/pi
400
Who was the first person to calculate pi?
Archimedes
500
Sketch then find the area. y=12-x^2, y=x^2-6
72
500
y=x^2, x=y^2; about y=1
11pi/30
500
Use shells to find the volume given by rotating the region bounded by the curves about the y-axis. y=e^-x^2, y=0, x=0, x=1
pi(1-1/e)
500
Anton Alejandro’s height in feet as he flies across the sky is modeled by the equation x^3 + 2x + 5, with x representing seconds from launch. Find the average value of his height after 5 seconds of flight.
165/4 feet
500
The world's northernmost capital is found in which Scandinavian country?
Iceland
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