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Example 9 Find

Example 9 Find

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Example 9 Find

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  1. Example 9 Find Solution We only know how to differentiate a an integral with a function of x in its upper bound. However, the given integral has functions of x in both of its bounds. Therefore, begin by using the additive property to write the given integral as the sum of two integrals, each with one constant bound: Before differentiating, interchange the bounds of the first integral: Let By the chain rule:

  2. By the First Fundamental Theorem of Calculus, the derivative F /(w) is obtained by replacing t by w in the integrand Apply this formula with w=u and with w=v:

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