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Given the partition $\{0,\frac{1}{4},\frac{1}{2},\frac{3}{4},1\}$ , find $L(P)$ and $U(P)$ for the integral $]\int_0^12x\,dx$ .

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Lesson Parent:

Problem:

Answer:

$L(P)=\frac{3}{4}$ and $U(P)=\frac{5}{4}$

Solution:

In each of these intervals, the minimum value of <Sign in to see all the formulas> will be used to find

$L(P)$ and the maximum value will be used to find

$U(P)$ .

Therefore,

and

This tells us that