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Estimate ? 3 0 f ( x ) g ? ( x ) d x if f ( x ) = x 2 and g ( x ) has the values given in...

Question:

Estimate {eq}\int_{0}^{3} f(x) g'(x) dx {/eq} if {eq}f(x) = x^2 {/eq} and {eq}g(x) {/eq} has the values given in the following table.

{eq}\begin{array}{l|c|c|c|c|c} x & 0 & 0.5 & 1 & 1.5 & 2 & 2.5 & 3 \\ \hline g(x) & 2.4 & 3 & 3.8 & 4.1 & 5 & 5.5 & 6 \end{array} {/eq}

Average Rate of Change:

Anytime the derivative is needed to be found but only two points are given, the average rate of change ({eq}\frac{f(b)-f(a)}{b-a} {/eq}) can measure how much the magnitude of a function increases or decreases between the two points, which is an approximation for the derivative.

Answer and Explanation: 1

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Given: {eq}\int_0^3 f(x) g'(x) dx \\ f(x) = x^2 \\ \begin{array}{l|c|c|c|c|c} x & 0 & 0.5 & 1 & 1.5 & 2 & 2.5 & 3 \\ \hline g(x) & 2.4 & 3 & 3.8...

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Average Rate of Change: Definition, Formula & Examples

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Chapter 20 / Lesson 5
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Finding the average rate of change is similar to finding the slope of a line. Study the definition of average rate of change, its formula, and examples of this concept.


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