Formula sheet
Applications of integrals — Formula Sheet
2 formulas from Calculus I, each with what it means, when to use it and the trap it sets.
Area between two curves
- What it says
- Upper curve minus lower curve, added up across the interval.
- When to reach for it
- The region trapped between two graphs.
- Watch out
- Find where they cross first — those are your limits, and the upper curve may swap on the other side of a crossing.
On [0,1] the line sits above the parabola throughout.
Volume by discs
- What it says
- Every thin slice is a circle of radius f(x); add up their areas along the axis.
- When to reach for it
- A region spun around an axis it actually touches.
- Watch out
- It is the square of the whole function, not the function of the square, and the π lives outside the integral.
y = x on [0,1] spun about the x-axis — a cone.
Other formula sheets
- Numbers and operations
- Algebra building blocks
- Lines and graphs
- Limits and continuity
- What a derivative is
- Differentiation techniques
- Applications of derivatives
- Integration
- Techniques of integration
- Sequences and series
- Parametric and polar
- Vectors and matrices
- Multivariable calculus
- Differential equations
- Probability and statistics