Mean value theorem for integrals
<p>The mean value theorem for integrals relates the area under a curve (the definite integral) to the mean value of that curve over the same interval. It is quite a simple theorem, in fact almost obvious, but other important theorems rely on it.</p>
<p>We will start with a graphical illustration before moving on to a precise statement and proof of the theorem.</p>
<h1>What is the mean value theorem?</h1>
<p>This graph shows the area under the curve <em>f(x)</em> between x-values <em>a</em> and <em>b</em> (ie a definite integral):</p>
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