# Find {eq}f {/eq}. {eq}f''(x) = x^{-2}, \quad x > 0, \quad f(1) = 0, \quad f(2) = 0 {/eq}.

## Question:

Find {eq}f {/eq}.

## Antiderivative:

The antiderivative of a continuous function {eq}q\left( x \right) {/eq} is {eq}\mu \left( x \right) {/eq} if {eq}\mu '\left( x \right) = q\left( x \right) {/eq}. A function {eq}q\left( x \right) {/eq} contains infinitely many antiderivatives in the expression {eq}\mu \left( x \right) + C {/eq}. Where, C is known as the constant of integration. Thus, {eq}\dfrac{d}{{dx}}\left\{ {\mu \left( x \right) + C} \right\} = \mu '\left( x \right) = q\left( x \right) {/eq}. The family of all antiderivatives is called the indefinite integral of the function {eq}q\left( x \right) {/eq}.

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Given

• The given function is {eq}f''\left( x \right) = {x^{ - 2}},x > 0,f\left( 1 \right) = 0,f\left( 2 \right) = 0 {/eq} .

Solution

Integrate...