The Fundamental Theorem of Calculus reduces the definite integral to an antiderivative. This topic is about what the definite integral computes — the physical, geometric, and economic objects it represents. The payoff in quantitative finance is concrete: consumer and producer surplus are the areas between demand-and-supply curves and the market price; probability densities integrate to cumulative probabilities and expected values; the average value of a function is the time-average portfolio return; and areas between curves are the geometric face of every "spread vs. threshold" question in fixed income and credit.
By the end of this topic you should be able to:
- compute the area between two curves by integrating the vertical (or horizontal) gap;
- set up and evaluate volumes of revolution using the disk/washer and cylindrical shell methods;
- compute work as the integral of a variable force, and the average value of a function over an interval;
- calculate consumer and producer surplus from demand and supply functions;
- integrate a probability density to compute probabilities, CDFs, expected values, and variance;
- compute arc lengths and surface areas using the arc-length formula.
In this lesson
- Contents
- The big picture
The full lesson is for members.
Read the full lessonNew to SelfMadeQuant.com? See membership options or explore the curriculum.