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Evaluate the given definite integral.$\int_{4}^{9} \sqrt{t} d t$

$$38 / 3$$

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 6

The Definite Integral

Integrals

Missouri State University

Campbell University

Baylor University

University of Michigan - Ann Arbor

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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Evaluate the integral.…

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Evaluate.$$\int_{4}^{9…

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Evaluate the given integra…

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06:48

Evaluate the integrals.

01:40

Evaluate the given indefin…

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01:09

don't be scared of this problem. Um, even though it's written as a square root understanding, rational exponents will save your life. Uh, we can rewrite this as to the one half power to one half power e t. Still, because then you can follow your rules of finding the anti derivative, and that would be adding one to your experiment. And if you need help with adding one to a fraction, just think about getting the same denominator to has is the same as as one. So that's how you got three houses and then multiply by the reciprocal of that new experience of two thirds from 4 to 9. Now, when you plug in those bounds, just remember that this means the square root of nine cubed. And I can also factor out that two thirds. I don't have to do that right away. So remember, it's the square root of nine cubed minus the square root of four cube. So if I'm looking at that, I can just quickly think, Oh, I swear to nine is three. Q. Give me 27 square to force two. Cubed is 82 times two attempts to so 27 minus eight. That's 19. So two thirds times 19 I can just multiply that 19. It's the numerator. Give me 38 thirds is your correct answer.

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