Math basics › Calculus II
Parametric and polar curves
Slope of a parametric curve
dy/dx = (dy/dt)/(dx/dt). Differentiate each part with respect to t, then divide.
Arc length
Length = ∫ √((dx/dt)² + (dy/dt)²) dt. It is Pythagoras on tiny pieces of the curve.
Area in polar
Area = ∫ ½r² dθ, not ∫ r dθ. The region is made of thin pie slices, and each slice has area ½r² dθ.
Finding the limits
For one loop, find the θ values where r = 0. The curve leaves the origin and comes back there.