计算:定积分∫(在上1 , 在下0)x⼀1+x^2 dx求详细过程答案,拜托大神...

2025-05-24 12:34:59
推荐回答(1个)
回答1:

∫(0→1) x/(1 + x²) dx
= (1/2)∫(0→1) d(1 + x²)/(1 + x²)
= (1/2)ln(1 + x²) |(0→1)
= (1/2)ln(1 + 1)
= (1/2)ln(2)