1922 Evaluate the definite integral by expressing it in termsof u and evaluating the

Chapter 5, Problem 21

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Evaluate the definite integral by expressing it in terms of $u$ and evaluating the resulting integral using a formula from geometry.

$\int_{x/3}^{\pi/2}\sin\theta\sqrt{1-4\cos^2\theta}\ d\theta;\quad u=2\cos\theta$

Equation Transcription:

$u$

$\int\limits_{\pi{}/3}^{\pi{}/2}\ \ sin\ \theta{}\ \sqrt{1\ -\ 4co{s}^{2}\ \theta{}}\ \ d\theta{};\ \ \ \ u\ =\ 2\ cos\ \theta{}$

Text Transcription:

int_{pi/3}^{pi/2} sin theta sqrt{1 - 4cos^2 theta} d theta; u = 2 cos theta

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