Mean value theorem of integral calculus

Application of the mean value theorem of differential calculus to the first two terms and the mean value theorem of integral calculus to each of the integrals of Eq. (13-82) followed by the limiting process whereby AZ is allowed to go to zero yields the following result upon recognition that Z and Z + AZ were selected arbitrarily in the domain (0 < Z < ZT) of interest... 

Theorem A-2-3 Mean value theorem of integral calculus If the function /(x) is continuous in the interval a [Pg.594]

Equation (5.83) is a version of the mean value theorem of integral calculus, which states that the mean value of a function is equal to the integral of the function divided by the length of the interval over which the mean is taken. 

Application of the mean value theorems of integral and differential calculus followed by the limiting process wherein AZ and AW are allowed to go to zero yields... 

In an attempt to find an exact formula for the integral, we may resort to the mean value theorem of calculus. This theorem states that if the integrand is evaluated at a particular known instant t = t between tn and tn+i, the integral is equal to f(T,tp(Ty)At. However, in the present case the theorem is of little use since the instant r is unknown. 

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