Application of Definite Integration

Four standard forms

Four standard forms: y² = 4ax (opens right), y² = -4ax (opens left), x² = 4by (opens up), x² = -4by (opens down). These forms help determine the orien

General form

General form: x²/a² + y²/b² = 1. When a > b, ellipse is wider horizontally; when a < b, ellipse is taller vertically. The area of any ellipse is πab s

For curve y = f(x) between

For curve y = f(x) between x = a and x = b: A = ∫[a to b] f(x) dx. For curve x = g(y) between y = c and y = d: A = ∫[c to d] g(y) dy. Choose the formu

For curves y = f(x)

For curves y = f(x) and y = g(x) intersecting at x = a and x = b, where f(x) ≥ g(x): A = ∫[a to b] [f(x) - g(x)] dx. Always subtract the lower curve f

When curve lies below x

When curve lies below x-axis, integral gives negative value. Take absolute value: |∫[a to b] f(x) dx|. For curves crossing x-axis, split at intersecti