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e) Answer any one :
i) Evaluate : ${\int }_0^{2\mathrm{\pi }}{e}^x \sin \left(\frac{\mathrm{\pi }}{4}+\frac{\mathrm{x}}{2}\right) dx.$

OR.



2.e (i) Ans: $-\frac{\sqrt{2}}{5}\left(e^{2\mathrm{\pi }}+1\right)$