Question

What is `f(x) = int -sinx dx` if `f(pi/3) = -6`?

Answer 1

`cosx-13/2`

Explanation:

`color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(intsinx dx=-cosx)color(white)(2/2)|)))`

`rArrint-sinxdx=cosx+c`

where c is the constant of integration.

We find c, using `f(pi/3)=-6`

`rArrcos(pi/3)+c=-6`

`rArr1/2+c=-6rArrc=-13/2`

`rArrF(x)=cosx-13/2`