Let be a continuous function such that

(1)

Evaluate the integral .

**Solution**

First of all we note that the equation

(2)

has a unique root , lets call it . Hence and thus . We note that is rewritten as

(3)

Integrating from to we get

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Let be a continuous function such that

(1)

Evaluate the integral .

**Solution**

First of all we note that the equation

(2)

has a unique root , lets call it . Hence and thus . We note that is rewritten as

(3)

Integrating from to we get