2024 MI PRU2 P1 Q3

2024 MI PRU2 P1 Q3

6 marks

Find \(\int x\mathrm{e}^{2x}\,\mathrm{d}x\).[3]
Hence find the exact value of \(\int_{-1}^{1} \left| x \right|\mathrm{e}^{2x}\,\mathrm{d}x\).[3]

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Answer:(i) \(\mathrm e^{2x}\left(\dfrac x2-\dfrac14\right)+C\) (ii) \(\dfrac{\mathrm e^2}{4}-\dfrac{3}{4\mathrm e^2}+\dfrac12\)

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