求f(x) f²(x)=∫f(t)sint/(2+cost)dt上限x下限0

问题描述:

求f(x) f²(x)=∫f(t)sint/(2+cost)dt上限x下限0

f²(x)=∫(0->x) f(t)sint/(2+cost) dt
2f(x) f'(x) = f(x) sinx/(2+cosx)
f'(x) = (1/2) sinx/(2+cosx)
f(x) = (1/2)∫ (0->x) [sint/(2+cost)] dt
= -(1/2) [ ln(2+cost)] (0->x)
= -(1/2) ( ln(2+cosx) - ln3)