Integration

Integration is an example of a numerical method/approximation

Anti-Differentiation

Antidifferentiation is just differentiation backwards
The derivative of sin is cos so the antiderivative of cos is sin

Fundamental Theorem of Calculus

The fundamental theorem of calculus states that differentation and integration are inverse operations.
The theorem provides a practical way of computing definite integrals
The theorem provides an algenraic method of computing many definite integrals without performing limit processes by finding formulas for antiderivatives.

If a function f is continuous on an interval [a-b] and if F is a function whose derivative is f on the interval [a-b] then:
for every x in the interval [a-b]

Area Under Curve

Negative Areas

Logarithmic

Trigonometric