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# Use the indicated entry in the Table of Integrals on the Reference Pages to evaluate the integral.$\displaystyle \int_0^1 \sqrt{x - x^2}\ dx$ ; entry 113

## $\int_{0}^{1} \sqrt{x-x^{2}} d x=\frac{\pi}{8}$

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Integration Techniques

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Okay, so this question wants us to evaluate this integral by using a formula from the table. So to do this, let's look at the formula on the table they want, which is this expression. So to do this, we need to turn our original expression into something that looks like this. So we see we have an X minus X squared, and we need to turn that into a to a U minus. You squared. So, to a has to equal one or a must be 1/2. So then plugging into the formula we see at the integral from 01 of X minus X squared is equal to Well, we just got a plug in 1/2 for a and we're evaluating this whole thing from 0 to 1 and then we'll see that this simplifies to 1/8 time's the co sign in verse of negative one, which is pie times on a or hi, divided by eight

University of Michigan - Ann Arbor

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Integration Techniques

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