Primitive of Pointwise Sum of Functions/Examples

Examples of Use of Primitive of Pointwise Sum of Functions

Primitive of $f + g$

Let $f$ and $g$ be real functions of $x$ which are integrable.

Then:

$\ds \int \paren {\map f x + \map g x} \rd x = \int \map f x \rd x + \int \map g x \rd x$

Primitive of $u + v + w$

Let $u$, $v$ and $w$ be real functions of $x$ which are integrable.

Then:

$\ds \int \paren {u + v + w} \rd x = \int u \rd x + \int v \rd x + \int w \rd x$

Primitive of $u + v - w$

Let $u$, $v$ and $w$ be real functions of $x$ which are integrable.

Then:

$\ds \int \paren {u + v - w} \rd x = \int u \rd x + \int v \rd x - \int w \rd x$

Primitive of $3 x \paren {2 x^2 + 5 x - 4}$

Primitive of Pointwise Sum of Functions/Examples/3x(2x^2 + 5x - 4)