The question is: Give an exakt value to P so that:

$\displaystyle IntP-sin^3v):dv = 1$ Int: limits are from $\displaystyle 0->pi$

$\displaystyle

sin3v = 3sinv-4sin^3v -> 4sin^3v = 3sinv-sin3v -> sin^3v = 3/4sinv-1/4sin3v

$

$\displaystyle Int(P-3/4sinv+1/4sin3v):dv$ from $\displaystyle 0;pi$

$\displaystyle

Int(P-3/4sinv+1/4sin3v):dv

$ = $\displaystyle (Pv+3/4cosv-3/4cos3v)$

$\displaystyle P(pi)+3/4+3/4-3/4-3/4 = 1$ -> $\displaystyle P(pi) = 1$ but the answer is $\displaystyle P = 7/3pi$