1 Limits

1.1 The Definition of Limit

1.2 Infinitesimals

2 Derivative And Differential

2.1 The Definition of Derivative

2.2 Rules of Finding Derivatives

2.3 The Definition of Differential

2.4 Implicit Function

2.5 First Order Linear Differential equations

2.6 Higher-Order Derivative And Taylor Series

3.1 The Definition of Integral

3.2 Riemann Sum and Definite Integrals

3.3 First Fundamental Theorem of Calculus

3.4 Second Fundamental Theorem of Calculus

3.5.1 Integrals of Trig Functions

3.5.2 Integrals of Radical Functions

3.5.3 Integrals of Rational Functions

3.6 Improper Integrals

3.7 Applications of the Integral

4.1 The Definition of Infinite Series

4.2 Important Infinite Series

4.3 The Test of Positive Series

4.4 The Test of Ordinary Series

On this page

$\int_{a}^{b} f (x) d x = F (b) - F (a)$

which $F (x)$ is the antiderivative of $f (x)$ , or $F^{'} (x) = f (x)$

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