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

Question

1704 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-10-06T18:51:22

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

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

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

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

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

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

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