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Evaluate the definite integral.$\int_{0}^{a} x \sqrt{a^{2}-x^{2}} d x$

$\frac{a^{3}}{3}$

Calculus 1 / AB

Calculus 2 / BC

Chapter 5

Integrals

Section 4

The Substitution Rule

Integration Techniques

Missouri State University

University of Michigan - Ann Arbor

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Lectures

01:11

In mathematics, integratio…

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Evaluate the definite inte…

07:17

Evaluate the integral.

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08:55

00:49

Evaluate the integrals…

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Evaluate the integrals.

05:19

Evaluate the integral.…

04:08

So if we let you is equal to a squared minus x square, we can let negative 1/2 to you is equal to x t X. Then we can rewrite are integral as negative 1/2 times the integral from a square to zero, um, of you to the power over 1/2 you this'd is just equal to negative 1/3 time's you to the power of three over two. Evaluated from a square, eight square to zero. Applying the second part of the fundamental rule of calculus, we end up that this is just equal to a cubed divided by three.

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