AP Calculus AB - Unit 6: Stuff to know
Multiple Choice
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17 Terms
When cross sections to base are squares
Integrand is squared (x)²
When cross sections to base are semicircles
Function is multiplied by π/2, Integrand is divided by two and squared, (x/2)²
When cross sections to base are isosceles right triangles
Function is multiplied by 1/4, Integrand is squared
When cross sections to base are equilateral triangles
Function is multiplied by (√3)/4, Integrand is squared
When cross sections are perpendicular to x-axis
Integral goes from a-b on the X-AXIS
When cross sections are perpendicular to y-axis
Integral goes from a-b on the Y-AXIS
When cross sections are circles (disks)
Function is multiplied by π, Integrand is squared
Half-Life Formula (1)
A(t) = A₀(1/2)ᵗ/ʰ
A = amount
A₀ = initial amount
t = time
h = half-life
Newton Cooling Formula (Derivative form)
dy/dt=k(y-Tₐ)
y = Temperature
k = Cooling Constant
t = time
Tₐ = Ambient Temperature
Exponential Growth/Decay Formula
y₁ = y₀eᵏᵗ
y₁ = amount
y₀ = initial amount
k = rate constant
t = time
Newton Cooling Formula
T(t) = Tₛ + (T₀ - Tₛ)e⁻ᵏᵗ
T = temperature
Tₛ = surrounding temperature
T₀ = initial temperature
k = rate constant
t = time
Trapezoidal Sum
Tₙ = ((b-a)/2n)*(y₀ + 2y₁ + 2y₂ + ……. + yₙ₋₁ + yₙ)
Newton’s Law of Cooling (Separated)
ln(T - Tₐ) = kt + C
T = temperature
Tₐ = surrounding temperature
k = rate constant
t = time
C = constant (determined by calculation)
General formula for the volume of a disk
V = pi integral a-b(r²)dx
r = radius, height of rectangular strip of the region
General formula for the volume of a washer
V = pi integral a-b(R²-r²)dx
R = outer radius, distance to the top of rectangular strip
r = inner radius, distance to the bottom of the strip
Annual Compounding Formula
A(t) = A₀(1+r)ᵗ
r = rate of interest
A₀ = initial amount
t = time
Continuous Compounding Formula
A(t) = A₀(1+(r/n))ⁿᵗ OR A(t) = A₀*eʳᵗ
n = number of times original amount is compounded
r = rate of interest
A₀ = initial amount
t = time
