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Integrate each of the given functions.$$\int \frac{y d y}{4 \sqrt{25-16 y^{2}}}$$

$-\frac{1}{64} \sqrt{25-16 y^{2}}+C$

Calculus 1 / AB

Chapter 28

Methods of Integration

Section 6

Inverse Trigonometric Forms

Integrals

Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

Boston College

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

01:34

Evaluate each integral.

01:21

Evaluate the integral.…

04:26

03:06

Evaluating integrals Evalu…

02:59

Evaluate each definite int…

01:38

10:23

Evaluate the following int…

00:58

Use a table of integrals t…

01:15

Evaluate the integrals.

02:50

Evaluate the integral.

we want to integrate the following expression the integral of Y. Dy divided by four square root 25 minus 16 1 square. This question is challenging our knowledge and understanding of integration techniques in particular is testing our newfound knowledge of inverse trig electric integral. These intervals are on the left one in the world. Do you over a squared minus U squared equals 16. You over A plus C. And on the right to Israel, do you over a squared plus B squared equals one over A. R. T and B over A plus C. Are integral clearly matches the form of integral one. Yeah. However we see that because in the denominator there's a 25-16-1 square and the numerator there's AY. Which means that if are you or why we wouldn't have why in the do you? It must be that we're actually gonna use the power rule. Until usually N. D. U equals U N plus one over N plus one will see. So we have that are integral values to 1/4 times negative 1/32 in a row negative 32 Y DY over Route 25 minute 61 squared equals 1/4 times negative. 1/32 times 2, 25 minute 61 squared plus C. Or negative 1/60 for 25 minutes. 16 1 squared plus C. The constant integration.

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