11.1 Flashcards
What is the formula for arc length of a curve given by y = f(x)?
L = the integral from a to b of
the square root of
(1+(dy/dx)^2) dx
What is the formula for the arc length of a parametric curve?
L = the integral from a to b of
the square root of
((dx/dt)^2 + (dy/dt)^2) dt
What is the formula for arc length of a polar curve?
L = the integral from θ1 to θ2 of
the square root of
(r(θ)^2 + (dr/dθ)^2) dθ
What is the formula for the area beneath a parametric curve?
The integral from a to b of
y(t) * x’ (t) dt
What is the formula for the derivative of a parametric curve?
dy/dt divided by dx/dt
What are the formulas associated with the equations of polar curves?
r = fθ
x = rcosθ
x = f(θ)cosθ
y = rsinθ
y = f(θ)sinθ
What is the formula for the derivative of a polar curve?
The derivative of rsinθ divided by the derivative of rcosθ
What is the formula for the area below a polar curve?
The integral from alpha to beta of 1/2 r^2 dθ
What is the parametric equation for a second derivative
dy’ / dt divided by dx/dt
When do you use method of disks and what is the formula?
It is used when rotating around an axis and slices are perpendicular to the axis of rotation
V is the integral of
Pi [f(x)]^2 dx
When do you use method of shells and what is the formula?
It is used when rotating around an axis and the slices are parallel to the axis of rotation
V is the integral of
2pi x*f(x) dx
