Solve problems about motion along a line using the power of integral calculus. For example, given the velocity of a particle as a function of time v(t), find how much the particle has traveled over a given time period.
We usually calculate the average of N terms by summing them up and dividing by N. How do you find the average of infinitely many terms? For example, the average of a function f(x) for all x-values between 0 and 1? Integral calculus to the rescue!