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Numerade Educator

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Problem 42 Medium Difficulty

Evaluate the integral.

$ \displaystyle \int^{1/\sqrt{2}}_{1/2} \frac{4}{\sqrt{1 - x^2}} \,dx $

Answer

$$
\frac{\pi}{3}
$$

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Video Transcript

Okay, The first thing we know we can do is we could take the four hours. It's a constant second off. We know we can recognize one thing one over the square root of one minus X squared. DX is actually equivalent to inverse sine of acts. Therefore, this is a property, so we know we have inverse sine of acts is actually are integral. Now we're at the point where we can plug in so four times in first sign of one over scored of two is four times pi over four. And then when we plug in one over, too, then we end up with pi over sex, which gives us pie mountains to power over three, which is just pie over three.