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Evaluate the given integral and check your answer.$$\int x^{3 / 4} d x$$

$$\frac{4}{7} x^{7 / 4}+c$$

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 1

Anti differentiation - Integration

Integrals

Missouri State University

Campbell University

Harvey Mudd College

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 given integra…

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Evaluate the integral and …

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Evaluate the integral.…

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03:48

And so we're looking at the integral of X to the three force Power DX, and I like the way they set it up. Because a zoo, long as you understand the anti derivative what you're doing, just add one to your exponents on. And then you multiply by the reciprocal of your new explosions and you'll get the correct answer. So we're already ready to do it because we have a rational exponents. Now, if you're bad at adding fractions, well, adding one shouldn't be too bad. But if you're having issues, just get the same denominator. Well, four forces equal toe one. So I think it's pretty clear from that that the numerator Sorry, uh, the exponent will be three plus 47 That denominator stays the same. And then you multiply by the reciprocal of that experiment, and then don't forget about plus seat. So this is your correct answer, and you can double check that. That's right, because you could take the derivative of that. And you, sir, reminder, you just move that expo in front. Well, you multiply 47 times, seven fours sevens. Cancel the force. Cancel. If you subtract one from that exponents get three fours and the drift of of the constant is zero. And that's why we need to have a plus C because there's an infinite number of correct answers because we can shift up and down. There's an infinite number of equations whose derivative is this, So that's why circling green is your correct answer.

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