Question 48

If $$f : R \rightarrow R$$ be a continuous function satisfying $$f(x) + f(3 - x) = 4$$, then $$\int_{0}^{3} f(x) dx$$ is equal to

Solution

$$\int_0^3f(x)dx=\int_0^3f(3-x)dx=A\left(say\right)$$ (using property of definite integrals).

Given $$f(x) + f(3 - x) = 4$$

Integrating with limit 0 to 3, we have

$$\int_0^3f(x)dx+\int_0^3f(x)dx=\int_0^34dx$$

$$A+A=4\left[3-0\right]$$

I=6.

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