Integration (Edexcel A-Level Mathematics): Flashcards

It links differentiation and integration concepts.

$F'(x) = f(x)$ if $F(x) = \int_a^x f(t) dt$.

Use $F(b) - F(a)$ for an antiderivative $F(x)$ of $f(x)$.

Integration can be undone by differentiation.

An antiderivative $F(x)$ satisfies $F'(x) = f(x)$.

$F(x)$ represents the accumulated area from $a$ to $x$.

Result: 63, from $[x^3]$ evaluated at 4 and 1.

The function $f(x)$ must be continuous on $[a, b]$.

The area between $f(x)$ and the $x$-axis from $a$ to $b$.

It profoundly impacts mathematics, physics, and engineering.