Hard problem with integrals

Jul 2008
13
4
Israel, Tel-Aviv
known
F(x)=int(f(arcsin(x)dx)
find
int(f(x)*cos(x)dx) between 0 to Pi
thought of t=sin(x) but i can only integrate for 0 to Pi/2...
 

Opalg

MHF Hall of Honor
Aug 2007
4,039
2,789
Leeds, UK
known
F(x)=int(f(arcsin(x)dx)
find
int(f(x)*cos(x)dx) between 0 to Pi
thought of t=sin(x) but i can only integrate for 0 to Pi/2...
It looks to me as though you have spotted an error in this question. The "known" function F(x) only provides information about f(t) in the interval \(\displaystyle |t|\leqslant \pi/2\). So you know nothing about f(x) for \(\displaystyle x>\pi/2\) and therefore there is no way that you can describe its integral in the interval \(\displaystyle [\pi/2,\pi]\).
 
Jul 2008
13
4
Israel, Tel-Aviv
It looks to me as though you have spotted an error in this question. The "known" function F(x) only provides information about f(t) in the interval \(\displaystyle |t|\leqslant \pi/2\). So you know nothing about f(x) for \(\displaystyle x>\pi/2\) and therefore there is no way that you can describe its integral in the interval \(\displaystyle [\pi/2,\pi]\).
is there a solution?