Question
Use the fact that the area of a circle of radius $r$ is $\pi r^{2}$ to evaluate the given definite integral. Sketch a region whose area is given by the definite integral.$$\int_{-5}^{5} \sqrt{25-x^{2}} d x$$
Step 1
This is because the equation of a circle is $x^{2}+y^{2}=r^{2}$, and if we solve for $y$, we get $y=\sqrt{r^{2}-x^{2}}$. In this case, $r^{2}=25$, so $r=5$. Show more…
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