Question

What is the antiderivative of `f(x) = 5`?

Answer 1

5x +c

Explanation:

Consider the `color(blue)"power rule for integration"`

`color(red)(|bar(ul(color(white)(a/a)color(black)(int(ax^n)dx=a/(n+1)x^(n+1))color(white)(a/a)|)))`

5 may be expressed as `5x^0`

and so `int(5x^0)dx=5/1x^(0+1)+c=5x+c` ( c is constant of integration.)

`rArrf(x)=5rArrF(x)=5x+c`