Problem

Evaluate the integral. $ \displaystyle \int^{…

02:53

Problem 41 Medium Difficulty

Evaluate the integral.

$ \displaystyle \int^{\sqrt{3}/2}_{0} \frac{dr}{\sqrt{1 - r^2}} $

Name: evaluate the integral displaystyle intsqrt32_0 fracdrsqrt1 r2
Uploaded: 2021-04-26
Duration: 1 min 43 s
Channel: Numerade
Description: Evaluate the integral. $ \displaystyle \int^{\sqrt{3}/2}_{0} \frac{dr}{\sqrt{1 - r^2}} $

Answer

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

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Video Transcript

this problem, I would just say to my students to memorize this rule. Otherwise there's a lot of math to work out um to really understand this would be a very long video. So I'm a keep this simple and I'm going to tell you ah that you could google or use your resources to look up the derivative of inverse sine. That's it's equal to this one over the square root of 1 -1. square. Uh So what I'm getting at is if we're going backwards then this anti drift will be inverse sine of our because that's the independent variable D. R. From 0 to Route 3/2. So as you plug in your upper bound and your lower bound, it's just saying like, okay, hey um if we're in the first quadrant we want the where the y coordinate on the unit circle is route 3/2. And that's at pi over three radiance. That's this angle. If if you remember your unit circle. And then the same thing is when you plug in zero Wins The Y Coordinate Equal to zero Radiance. Well the white cord and zero at zero radiance. I said that wrong. So when you plug in zero you actually do get zero. So your answers pirate 3 0, which is simply pi over three. Now I'm just double checking before I move on. Yes, that is the correct answer.

Gregory H.

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Integrals

Integration

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Integrals

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