![]() ![]() Now suppose we are given an acceleration function a, a, but not the velocity function v v or the position function s. ![]() Furthermore, the acceleration a ( t ) a ( t ) is the derivative of the velocity v ( t ) v ( t )-that is, a ( t ) = v ′ ( t ) = s ″ ( t ). ![]() In our examination in Derivatives of rectilinear motion, we showed that given a position function s ( t ) s ( t ) of an object, then its velocity function v ( t ) v ( t ) is the derivative of s ( t ) s ( t )-that is, v ( t ) = s ′ ( t ). Here we examine one specific example that involves rectilinear motion. Why are we interested in antiderivatives? The need for antiderivatives arises in many situations, and we look at various examples throughout the remainder of the text. The antiderivative of a function f f is a function with a derivative f. We answer the first part of this question by defining antiderivatives. We now ask a question that turns this process around: Given a function f, f, how do we find a function with the derivative f f and why would we be interested in such a function? 4.10.4 Use antidifferentiation to solve simple initial-value problems.Īt this point, we have seen how to calculate derivatives of many functions and have been introduced to a variety of their applications.4.10.3 State the power rule for integrals.4.10.2 Explain the terms and notation used for an indefinite integral.4.10.1 Find the general antiderivative of a given function. ![]()
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