求f(x) f²(x)=∫f(t)sint/(2+cost)dt上限x下限0
人气:429 ℃ 时间:2019-12-09 11:19:01
解答
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)
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