Integration

Integration reverses differentiation and measures accumulation. From antiderivatives to the Fundamental Theorem, this chapter builds the bridge between the two halves of calculus.

Lessons

Lesson 1 · G12 5.1

Antiderivatives

Reverse differentiation; the indefinite integral.

Open lesson → Lesson 2 · G12 5.2

Sums and Sigma Notation

Compact notation for sums, telescoping.

Open lesson → Lesson 3 · G12 5.3

Area

Riemann sums and the area problem.

Open lesson → Lesson 4 · G12 5.4

Definite Integrals

Formal definition as a limit of sums.

Open lesson → Lesson 5 · G12 5.5

Fundamental Theorem of Calculus

Linking antiderivatives to definite integrals.

Open lesson → Lesson 6 · G12 5.6

Integration by Substitution

Reversing the chain rule.

Open lesson → Lesson 7 · G12 5.7

Numerical Integration

Trapezoidal rule, Simpsons rule.

Open lesson → Lesson 8 · G12 5.8

The Natural Logarithm as an Integral

Defining ln x via an integral.

Open lesson →