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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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01:24

Frank Lin

Calculus 1 / AB

Chapter 5

Integrals

Section 5

The Substitution Rule

Integration

Campbell University

Harvey Mudd College

Baylor University

Boston College

Lectures

05:53

In mathematics, an indefinite integral is an integral whose integrand is not known in terms of elementary functions. An indefinite integral is usually encountered when integrating functions that are not elementary functions themselves.

40:35

In mathematics, integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. Given a function of a real variable (often called "the integrand"), an antiderivative is a function whose derivative is the given function. The area under a real-valued function of a real variable is the integral of the function, provided it is defined on a closed interval around a given point. It is a basic result of calculus that an antiderivative always exists, and is equal to the original function evaluated at the upper limit of integration.

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Use a graph to give a roug…

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Evaluate the area under ea…

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Find the area of the regio…

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

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