Please tell me what did I do wrong on this integration. The book claimed this can only be solved in numerical method and the answer is 1.218.(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\int _0^{\pi} \frac {\cos ^2\left [\frac {\pi} 2 \;\cos\;\theta\right]}{\sin \theta}\;d\;\theta [/tex]

[tex]\hbox { Let }\; u=\frac {\pi} 2\; \cos \theta\;\Rightarrow\; d\theta =-\frac{2\;d\;u}{\pi\;\sin\;\theta}\; \Rightarrow\;\int _0^{\pi} \frac {\cos ^2\left [\frac {\pi} 2 \;\cos\;\theta\right]}{\sin \theta}\;d\;\theta \;=\; -\frac 2 {\pi}\int \cos^2\;u \;d\;u\;=-\frac 1 {\pi} \left[ \int d\;u \;+\; \int \cos(2u) d\;u \right ][/tex]

[tex] = -\left [\frac { \frac {\pi} 2 \cos \theta}{\pi}\right]_0^{\pi} \;-\;\frac 1 {2\pi} \int \cos v \;dv \;\;\;\;\;\;\hbox { where }\;\; \;v=2u \;\hbox { and }\;d\;u=\frac {d\;v} 2 [/tex]

[tex]= 1 -\left[\frac { \sin (2\frac {\pi} 2 \;\cos \theta)}{2\pi}\right]^{\pi}_0 \;= 1 [/tex]

I solve this without using numerical method and the answer is 1 instead of 1.218. Who is right?

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# Homework Help: Please help in an integration

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