Velocity, Acceleration and Displacement: Formulas and Graphs
Velocity, acceleration and displacement explained: average and instantaneous formulas, motion graphs, calculus links and worked examples.
Category: Applications
Read article → Velocity, Acceleration and Displacement: Formulas and Graphs
Projectile Motion: Equations, Range and Max Height
Projectile motion explained: velocity components, time of flight, range, maximum height and the parabolic path, with calculus derivations and examples.
Polar Coordinates and Polar Equations: Graphs, Area, Slope
Polar coordinates explained: polar-rectangular conversion, graphing polar equations (circles, cardioids, roses), slope, area and arc length.
Kinematic Equations: The 5 Suvat Formulas with Examples
The five kinematic equations for constant acceleration, how to pick the right one, where they come from in calculus, and worked free-fall and braking examples.
Optimization Problems in Calculus: 4 Solved Examples
Solve calculus optimization problems in 6 steps. Worked examples: the largest fenced area, the open box, the cheapest can and the closest point on a curve.
Related Rates: Step-by-Step Strategy and Classic Problems
Solve related rates problems in 6 steps. Worked classics: the sliding ladder, the expanding balloon, the draining cone and the moving shadow.
Area Between Two Curves: Step-by-Step Method and Examples
Area between curves = ∫(top − bottom)dx. Find intersection points, handle curves that cross, and integrate with respect to y when easier. Worked examples.
Riemann Sums: Left, Right, Midpoint and Simpson’s Rule
How to compute left, right and midpoint Riemann sums, the trapezoidal rule and Simpson’s rule, with a full worked example and error comparison.
Average Value of a Function: Formula, Meaning and Examples
The average value of f on [a, b] is (1/(b − a))∫f(x)dx. Why the formula works, examples with sin x, x² and eˣ, and the Mean Value Theorem for integrals.
Shell Method for Volume: Formula, Examples and Disk vs Shell
The shell method finds volumes of revolution with V = 2π∫(radius)(height)dx. Step-by-step examples and a clear guide to choosing shells or disks.