Let be a continuous function such that

(1)

Prove that there exists a such that

**Solution**

Define . Then, integrating by parts it follows that

By the mean value theorem for integrals, there is a point in such that , i.e.

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Let be a continuous function such that

(1)

Prove that there exists a such that

**Solution**

Define . Then, integrating by parts it follows that

By the mean value theorem for integrals, there is a point in such that , i.e.