请问各位大神，这个第十题怎么做? 第1页

Since is continuous on the interval while , so by the 's inequality, we have

In fact, this inequality is a side of the so-called 's inequality:

's inequality.
Let be continuous on the interval , and Then holds

Formerly we've proved the left side, now we try to illustrate the right side.

Note that

i.e.

Integrate by two sides, we get

From inequality, we know

Thus

Actually, we could even generalize the 's inequality to

Generalized 's inequality.
Let be continuous on the interval , and while is a real constant. Then there holds