Free module · Calculus & mathematical models
Integral Calculus: Accumulation & Area
Build totals from rates, reverse differentiation, and understand continuous averages.
Riemann sums · antiderivatives · substitution · integration by parts
The building blocks
- An integral adds small contributions.
- Begin with a constant rate, where the total is a rectangle.
- Add rectangular contributions
- Connect area to antiderivatives
- Choose exact or numerical integration
Lessons in this module
- Start with rectangles: rate × time = amount
- Definite integrals: adding many small contributions
- Core integral rules: undo a derivative, then check
- Antiderivatives and the fundamental theorem
- Integration techniques: substitution and integration by parts
- Improper integrals, densities and continuous expectations
- Numerical integration and a continuous cash-flow building block
Practice and apply
- Integrate a rate and recover a level — Flow q(t)=2t litres/minute from t=0 to t=3 minutes. Initial tank volume is 5 litres.
- Constant accumulation — Flow is 4 litres/minute for 3 minutes. Find total volume.
- Find the coefficient — An antiderivative of 6x² is ax³. Find a.
Work through the practice exercises · Quant development tools