Using integration by parts, show that\n\(\n\int e^{2x}\sin x\,dx=e^{2x}\left[A\sin x+B\cos x\right]+C,\n\)\nwhere \(A\), \(B\) and \(C\) are arbitrary constants to be determined.[4]
A curve \(C_2\) has equation \(y=e^{2x}\sin x\). Show that the exact area of the region bounded by \(C_2\), the \(x\)-axis and the lines \(x=-1\) and \(x=1\) can be expressed as\n\(\n\alpha+\beta\sin(1)+\delta\cos(1),\n\)\nwhere \(\alpha\), \(\beta\) and \(\delta\) are exact constants to be determined.[3]
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