inequalities for integrals.

Nov 2019
22
1
UK
Hello,

stuck on this question, is anyone able to help?

Prove that (π /3(1 + √ 3 )) ≤ (the integral from pi/6 to pi/3 of) (1+2 sin x)/ (1 + 2 cos x) dx ≤( π / 12) (1 + √ 3 ).

Thanks
 
Dec 2015
1,078
166
Earth
\(\displaystyle \sin(x) =2T/(1+T^2 )\) ; \(\displaystyle \cos(x)=(1-T^2 )/(1+T^2 )\) , where \(\displaystyle T=\tan(x/2)\) and \(\displaystyle dx=2dT/(1+T^2 )\).
Evaluate the integral first.
 
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