JEE Advance - Mathematics (2005 - No. 9)
Evaluate $$\,\int\limits_0^\pi {{e^{\left| {\cos x} \right|}}} \left( {2\sin \left( {{1 \over 2}\cos x} \right) + 3\cos \left( {{1 \over 2}\cos x} \right)} \right)\sin x\,\,dx$$
$$\frac{24}{5}\left[e\cos \left(\frac{1}{2}\right) + \frac{1}{2}e\sin \left(\frac{1}{2}\right) - 1\right]$$
$$\frac{12}{5}\left[e\cos \left(\frac{1}{2}\right) + \frac{1}{2}e\sin \left(\frac{1}{2}\right) - 1\right]$$
$$\frac{24}{5}\left[e\cos \left(\frac{1}{2}\right) - \frac{1}{2}e\sin \left(\frac{1}{2}\right) - 1\right]$$
$$\frac{24}{5}\left[e\cos \left(\frac{1}{2}\right) + \frac{1}{2}e\sin \left(\frac{1}{2}\right) + 1\right]$$
$$\frac{24}{5}\left[\cos \left(\frac{1}{2}\right) + \frac{1}{2}\sin \left(\frac{1}{2}\right) - 1\right]$$
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