Calc Unit 8 Equations

Question 1

Disk method equation

Answer 1

Pi a-int-b (f(x)^2)dx

Question 2

Washer equation

Answer 2

Pi a-int-b {[f(x)]^2 - [g(x)]^2} dx

Question 3

Area between two curves

Answer 3

A = a-int-b [f(x) - g(x)] dx

Question 4

Average value function

Answer 4

(1/b-a) a-int-b [f(x)] dx

Question 5

Int of velocity

Answer 5

Displacement or net change

Question 6

Int of |velocity|

Answer 6

Total distance

Question 7

|velocity|

Answer 7

Speed

Question 8

Derivative of position

Answer 8

Velocity

Question 9

Derivative of velocity

Answer 9

Acceleration

Question 10

Square cross sections

Answer 10

V = a-int-b [s^2] dx
s = [f(x)-g(x)]
Where f(x) > g(x)

Question 11

Rectangular cross section

Answer 11

V = a-int-b (width * height) dx
Width = f(x) - g(x)
Height = given in the problem

Question 12

Equalateral triangle cross section

Answer 12

V = a-int-b [A(x)] dx
A = (3sq./4)s^2
s = f(x) - g(x)

Question 13

Isosceles right triangle

Answer 13

V = a-int-b [A(x)] dx
A = [f(x) - g(x)]/2

Question 14

Semicircle cross section

Answer 14

V = a-int-b [A(x)] dx
A = 1/2 pi r^2

Question 15

Quarter circle cross section

Answer 15

V = a-int-b [A(x)] dx
A = 1/4 pi r^2