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      <text>10.3.8 (Antiderivatives)</text>
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      <text><![CDATA[<h3>Antiderivatives</h3>

<p>We will now change tack somewhat and introduce the concept of an <i>antiderivative</i>. It will become apparent in the next section why we require this slight deviation. As you may suspect from the name, an antiderivative of the function \(f(x)\) is a function whose derivative is \(f(x)\). So if \(F(x)\) is an antiderivative of \(f(x)\) then \(F'(x)=f(x)\). You can think of the antiderivative as the result of "undoing" differentiation, or as the inverse of differentiating.</p>
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<p style="text-align: center;"><img src="@@PLUGINFILE@@/4_0_3antideriv.svg" alt="Derivative is x^2, antiderivative is (1/3)*x^3" width="355" height="96" class="img-responsive atto_image_button_text-bottom"></p>
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<h3>Example</h3>

<p>Find an antiderivative of \(\cos(x)\).</p>

<b>Solution</b>

<p>Since \(\dfrac{d}{dx}\sin(x)=\cos(x)\), we have that \(\sin(x)\) is an antiderivative of \(\cos(x)\). nNote that since&nbsp;\(\dfrac{d}{dx}\left(\sin(x)+5\right)=\cos(x)\), we also have that \(\sin(x)+5\) is an antiderivative of \(\cos(x)\). In fact, there are many possible antiderivatives.</p>]]></text>
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