CH 5 - Definite Integral In Science

Question 0

Equation for volume via disks

Answer 0

dV = pi * r^2 dx

Question 1

Equation for the area between two curves

Answer 1

Difference between the definite integrals from a to b

Question 2

Equation for volume via washers

Answer 2

dV = pi * [R^2 - r^2] dx

Question 3

Equation for volume via cylindrical shells

Answer 3

dV = 2pix*f(x) dx

Question 4

Equation for the length of a curve

Answer 4

dL = sqrt(1+(dy/dx)^2) dx

Question 5

Equation for the surface area of a rotated curve

Answer 5

dS = 2piy*sqrt(1+(dy/dx)^2) dx

Question 6

Equation to define Work

Answer 6

W = F*d
Work = Force * distance
Weight = force

Question 7

Equation for work with a variable force

Answer 7

W = F(x) dx

Question 8

Hooks law for spring constant

Answer 8

F = kx

Where k is the constant and x is the distance past the natural rest position

Question 9

SI and BE units for:

Force * Distance = Work

Answer 9

SI: Newton * Meters = Joule
BE: Pounds * foot = FtLbs

Question 10

Equation for pressure

Answer 10

P = F/A
Pressure = Force/Area
Force in weight*distance (Newtons or FtLbs)

Question 11

Equation for fluid force

Answer 11

dF = ρh(x)w(x) dx

Where ρ is fluids weight density, h(x) is depth of point x, and w(x) is width of surface at point x