Find {eq}f {/eq}.

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


Find {eq}f {/eq}.

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


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



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Antiderivative: Rules, Formula & Examples


Chapter 8 / Lesson 12

Understand what an antiderivative is and what antiderivative rules are. Use various antiderivative formulas and learn how to do antiderivatives. See the antiderivative chart for common functions and practice solving basic antiderivatives examples.

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