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Numerade Educator



Problem 75 Hard Difficulty

Use a graph to give a rough estimate of the area of the region that lies under the given curve. Then find the exact area.

$ y = \sqrt{2x + 1} $, $ 0 \le x \le 1 $



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Video Transcript

okay said this area over here is the shaded region. We know we can estimate this to be approximately 1.4 squares because this is one. And then if this is too, this is like 1.41 point five. So 1.4 times one is one is 1.4. Now we're finding the exact area. As you can see it we made. Are you two experts? One to get 1/2? Do you? Is dio is detox usually the US What's under the square root, which you can see from my calculations. Now we're going to be using the power rule, which means we increase the exploited by one, and we divide by the new exponents. Okay, Now that I've done that, we can plug in roundup with square root of three minus 1/3 which, if you're not sure what this says, you can plot a calculator and you'll get approximately 1.3987 So this is very close to 1.4