高数求微积分紧急求大虾们第二部到第三部怎么计算得到.求给出稍微详细点的解题步骤
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高数求微积分
![](http://img.wesiedu.com/upload/d/9b/d9b77da74c9138c59b965579633c7104.jpg)
紧急求大虾们第二部到第三部怎么计算得到.求给出稍微详细点的解题步骤
![](http://img.wesiedu.com/upload/d/9b/d9b77da74c9138c59b965579633c7104.jpg)
紧急求大虾们第二部到第三部怎么计算得到.求给出稍微详细点的解题步骤
![高数求微积分紧急求大虾们第二部到第三部怎么计算得到.求给出稍微详细点的解题步骤](/uploads/image/z/3021911-71-1.jpg?t=%E9%AB%98%E6%95%B0%E6%B1%82%E5%BE%AE%E7%A7%AF%E5%88%86%E7%B4%A7%E6%80%A5%E6%B1%82%E5%A4%A7%E8%99%BE%E4%BB%AC%E7%AC%AC%E4%BA%8C%E9%83%A8%E5%88%B0%E7%AC%AC%E4%B8%89%E9%83%A8%E6%80%8E%E4%B9%88%E8%AE%A1%E7%AE%97%E5%BE%97%E5%88%B0.%E6%B1%82%E7%BB%99%E5%87%BA%E7%A8%8D%E5%BE%AE%E8%AF%A6%E7%BB%86%E7%82%B9%E7%9A%84%E8%A7%A3%E9%A2%98%E6%AD%A5%E9%AA%A4)
令 (1-r/R)^(1/n) = t,则 1-r/R = t^n,r=R(1-t^n),dr=-nRt^(n-1)dt
于是 [2πu/(πR^2)]∫(1-r/R)^(1/n)rdr
= (2u/R^2)∫ t[-nRt^(n-1)]R(1-t^n)dt
= (2nu)∫t^n(1-t^n)dt
= (2nu)∫[t^n-t^(2n)]dt
= (2nu)[t^(n+1)/(n+1)-t(2n+1)/(2n+1)]
= 2nu*n/[(n+1)(2n+1)]
= 2n^2u/[(n+1)(2n=1)].
于是 [2πu/(πR^2)]∫(1-r/R)^(1/n)rdr
= (2u/R^2)∫ t[-nRt^(n-1)]R(1-t^n)dt
= (2nu)∫t^n(1-t^n)dt
= (2nu)∫[t^n-t^(2n)]dt
= (2nu)[t^(n+1)/(n+1)-t(2n+1)/(2n+1)]
= 2nu*n/[(n+1)(2n+1)]
= 2n^2u/[(n+1)(2n=1)].