(ii) Evaluate: ∫0^(π)/(2)(sin 2 x)/(sin ^4 x+cos ^4 x) d x.

Name: (ii) Evaluate: ∫0^(π)/(2)(sin 2 x)/(sin ^4 x+cos ^4 x) d x.
Uploaded: 2020-08-27T00:01:52-08:00
Duration: 2 min 53 s
Channel: Bryan Lynn
Description: (ii) Evaluate: ∫0^(π)/(2)(sin 2 x)/(sin ^4 x+cos ^4 x) d x.

First, let's simplify the integrand. We can rewrite the denominator as (sin^4 x + cos^4 x = (

Question

(ii) Evaluate: \( \int_{0}^{\frac{\pi}{2}} \frac{\sin 2 x}{\sin ^{4} x+\cos ^{4} x} d x \).

          (ii) Evaluate: \( \int_{0}^{\frac{\pi}{2}} \frac{\sin 2 x}{\sin ^{4} x+\cos ^{4} x} d x \).

(ii) Evaluate: ∫0^(π)/(2)(sin 2 x)/(sin ^4 x+cos ^4 x) d x.

Added by Carlos B.

Fundamentals of Differential Equations

R. Kent Nagle 9th Edition

Chapter 6

Instant Answer

Solved by Expert Bryan Lynn

08/27/2020

Step 1

We can rewrite the denominator as \(\sin^4 x + \cos^4 x = (\sin^2 x)^2 + (\cos^2 x)^2\). Using the identity \(\sin^2 x + \cos^2 x = 1\), we can rewrite the denominator as \(1 - 2\sin^2 x \cos^2 x\). Now, let's rewrite the numerator. We can use the double angle Show more…

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