textbook-theory · English
Distance, Position, and the Length of Curves
Section 4.8 from Dan Sloughter's open calculus textbook 'Difference Equations to Differential Equations,' covering three applications of definite integrals: computing distance traveled from a velocity function, recovering position from velocity and initial conditions via the Fundamental Theorem of Integral Calculus, and deriving the arc-length integral formula for plane curves. The section includes worked examples involving oscillating springs, numerical integration, and curves such as y = x^(3/2), y = x^2, and y = sin(x), along with a ten-problem exercise set.
definite integralsarc lengthkinematicscalculus