Slope Fields
Area Under a Curve
Volume using the Disk Method
Volume using the Washer Method
Volume with known Crossections
100
What is another name for "slope fields?"
Direction Fields
100
What is the general equation for finding the area between two curves?
A=∫_a^b▒[f(x)-g(x)]dx
100
What is the equation for finding the volume of a solid of revolution using the disk method?
V=π∫_a^b▒〖[R(x)]^2dx〗
100
What is the equation for finding the volume of an area using the washer method?
V=π∫_a^b▒([R(x)]^2-[r(x)]^2 )dx
100
What is the equation for the volume with the area taken perpendicular to the x-axis?
V=∫_a^b▒A(x)dx
200
What do slope fields show?
the general shape of all solutions of a differential equation
200
When finding the area, do you subtract the bottom from the top, or the top from the bottom?
Top-Bottom
200
What is the resulting solid created by a region in a plane that is revolved about a line called?
a solid of revolution
200
Find the volume of the solid generated by revolving the region bounded by the graphs of y=x^1/2, y=0, and x=3 around the line x=3.
(24pi3^1/2)/5
200
What is the equation for the volume with the area taken perpendicular to the y-axis?
V=∫_c^d▒A(y)dy
300
How are slope fields usually drawn?
Using a graphing utility
300
Find the area of the region bounded by y=x^2-1, y=-x+2, x=0, and x=1.
13/6 units squared
300
Find the volume of the solid generated by revolving the region bounded by the graphs of y=x^1/2, y=0, and x=3 around the x-axis.
9pi/2
300
Find the volume of the solid generated by revolving the region bounded by the graphs of y=x^1/2, y=0, and x=3 around the line x=6.
(84pi*3^1/2)/5
300
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations around the x-axis. y=1/x, y=0, x=1, x=3.
2pi/3
400
How are slope fields used in calculus?
They give a visual perspective of the directions of the solutions of differential equations.
400
Find the area of the region bounded by y=(1/2)x^3+2, y=x+1, x=0, and x=2
2 units squared
400
Find the volume of the solid generated by revolving the region bounded by the graphs of y=x^2, y=4x-x^2 around the x-axis.
32pi/3
400
Find the volume of the solid generated by revolving the region bounded by the graphs of y=x, y=3, and x=0 around the line y=4.
18pi
400
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the y-axis. y=3(2-x), y=0, x=0.
8pi
500
Can you derive an exact equation from a slope field?
No, you cannot tell exactly where the graph, just its general shape
500
Find the area of the region between the graphs of f(x)=3x^3-x^2-10x and g(x)=-x^2+2x
24 units squared
500
Find the volume of the solid generated by revolving the region bounded by the graphs of y=x^1/2, y=0, and x=3 around the y-axis.
(36pi*3^1/2)/5
500
Find the volume of the solid generated by revolving the region bounded by the graphs of y=3/(1+x), y=0, and x=0 around the line y=4.
pi(48ln2-27/4), or around 83.318
500
Find the volume of the solid generated by revolving the region bounded the graphs of the equations about the x-axis. y=2arctan(.2x), y=0, x=0, x=5.
15.4115
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