The function s(t) represents the position of an object at time t moving along a line. Suppose...

Question:

The function s(t) represents the position of an object at time t moving along a line. Suppose s(2) = 136 and s(3) = 156. Find the average velocity of the object over the interval of time {eq}\left [ 1, 4 \right ] {/eq}.

Average Value of a Function

One of the methods to compute the average value of a function is through definite integrals. The average value of a function {eq}f(x) {/eq} defined on the interval {eq}[a,b] {/eq} is given by {eq}\displaystyle \bar{f} = \frac{1}{b-a} \int_a^b f(x) \text{ d}x {/eq}.

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Let's get the equation for the position of the object in terms of time {eq}t {/eq}. Since it is moving along a line, its position equation is linear.... Evaluating Definite Integrals Using the Fundamental Theorem

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Chapter 16 / Lesson 2
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In calculus, the fundamental theorem is an essential tool that helps explain the relationship between integration and differentiation. Learn about evaluating definite integrals using the fundamental theorem, and work examples to gain understanding.