Question

What is `f(x) = int -cos2x dx` if `f(pi/3) = 0`?

Answer 1

`f(x)=-1/2sin2x+sqrt3/4.`

Explanation:

`f(x)=int-cos2xdx=-(sin2x)/2+C`

To determine `C`, we make use of the cond. that, `f(pi/3)=0`

`f(pi/2)=0 rArr -1/2sin(2(pi/3))+C=0`

`:. C=1/2sin(pi-pi/3)=1/2sin(pi/3)=1/2*sqrt3/2=sqrt3/4`

`:. f(x)=-1/2sin2x+sqrt3/4.`