#anti-derivative

[math-journal2]

4.1

Integration by Parts

[math-journal2]

2.1

Intro to Integration

[math-journal2]

<— 1.1 —>

Introduction to:

Anti-Derivatives

When they say “any anti-derivative” vs “general anti-derivative” is this:

sin(x) + c —> general

sin(x) + 1; sin(x) —> 2 examples of any

Rarely did my prof ask you for any since there’s a billion things you could say.

[drcyrus]

The Fundamental Theorem of calculus

if f is continous on an open interval containing a and x and then we first integrate the function f and then differentiate with respect to x, then the result we get is the function f again.

Suppose that f is continuous at a closed interval [a,b] if the function F is defined on a closed interval [a, b] by where a is a real number, Then F is the anti-derivative of f. in other words, F'(x) = f(x) consider the relationships: then f(x) = x2 and Note: We use the dummy variable (t) in the integrand to avoid confusion with the upper limit x. Sometimes the fundamental theorem of…

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