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Evaluate the given integral and check your answer.$$\int \frac{1}{\sqrt{x}} d x$$

$$2 \sqrt{x}+c$$

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 1

Anti differentiation - Integration

Integrals

Missouri State University

University of Michigan - Ann Arbor

University of Nottingham

Idaho State University

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.

01:34

Evaluate the given integra…

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Evaluate the integral.…

00:53

Evaluate the indefinite in…

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02:01

Find the Integral

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Find the Integral of \int …

01:36

Evaluate the following int…

All right. So we're asked to find the integral of one over the square root of X. Okay, um, DX and all. I would tell my students when they're first learning. This is to practice your rational exponents. Eso just rewrite the problem with a X being in the denominator. Make it a negative power. And the square root is the same thing as a one half power DX. So this is just algebra manipulation. So then you can do the process of the anti derivative, which is adding one to your exponents. Add one to your exponents and then multiply by the reciprocal. So we're ready to find the the integral eso. If you need help adding one to negative one half, just think about getting the same denominator. So two halves is equal to one. Well, negative one plus two is one denominator stays the same, uh, and then multiply by the reciprocal of one half. So that would be, too. And don't forget about plus seat. And this is your correct answer. Now they do want you to check your work. And that would be easy, because you could just take the derivative of the answer. You just found. This is why we do a plus c in here. First of all, multiply that exponents by the coefficient and half of two is one. And you subtract one from your exponents. One half minus one is number one half and a derivative of the constant is zero eso. This confirms that we get the same answer. And that's why we need this as our answer. Circling grain is correct.

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