# Given f(x) = \frac{3x^2 - 5}{(x^3-5x+1)^2} You can check that on the interval (2,3) the...

## Question:

Given {eq}f(x) = \dfrac{3x^2 - 5}{(x^3-5x+1)^2} {/eq} You can check that on the interval (2,3) the function is never negative.

a) Determine an antiderivative of the function and use it to calculate {eq}\displaystyle\int^3_2 f(x)dx {/eq}.

## Definite Integral

As the name implies, this integral is defined within certain ( and hence definite) bounds of the independent variable. Definite integration has numerous applications in real life. A couple of examples are estimating the area bounded by two or more curves or finding the center of gravity of an object.

## Answer and Explanation:

{eq}\displaystyle f(x) = \frac{3x^2 - 5}{(x^3-5x+1)^2}. {/eq}

We know that square of all real numbers is positive. So the sign of {eq}f(x){/eq}...

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from AP Calculus AB & BC: Homework Help Resource

Chapter 13 / Lesson 13