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}.
{eq}f''(x) = x^{-2}, \quad x > 0, \quad f(1) = 0, \quad f(2) = 0 {/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}.
Answer and Explanation: 1
Become a Study.com member to unlock this answer! Create your account
View this answerGiven
- 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...
See full answer below.
Learn more about this topic:
from
Chapter 8 / Lesson 12Understand 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.