英语翻译find the average rate of change of the function over the

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英语翻译
find the average rate of change of the function over the given intervals
f(x)=x^3 + 1
[2,3] [-1,1]
g(t)= 2 + cos(t)
[0,∏] [-∏,∏]
只有翻译也可以
怎么求不规则曲线两点间的平均值呢?
只有解答也可以

翻译:
求以下函数在所给区间的平均变化率
一点上的变化率就是一次导数,平均变化率就是：
对倒数在该区间积分 / 区间长度.
所以,f(x)在[2,3]的平均变化率=[f(3)-f(2)]/(3-2)=19
f(x)在[-1,1] 的平均变化率=[f(1)-f(-1)]/(1+1)=1
g(t)在[0,∏]的平均变化率=[g(∏)-g(0)]/(∏-0)=-2/∏
[-∏,∏] g(t)在[-∏,∏] 的平均变化率=[g(∏)-g(-∏)]/(∏+∏)=0

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