Find $\displaystyle\displaystyle \displaystyle\int (2x-1) \cos x \, \mathrm{d}x$.[3] Hence find th

Question

Find $\displaystyle\displaystyle \displaystyle\int (2x-1) \cos x \, \mathrm{d}x$.[3] Hence find the value of $\displaystyle\displaystyle \displaystyle\int_{0}^{\frac{\pi}{2}} |2x-1| \cos x \, \mathrm{d}x$. Give your answer in the form $A-4 \cos B$, where $A$ and $B$ are exact constants to be determined.[4]

Accepted Answer

(a) $(2x-1)\sin x+2\cos x+c$. (b) $\displaystyle\int_0^{\pi/2}|2x-1|\cos x\,\mathrm{d}x=\pi+1-4\cos\frac12$, so $A=\pi+1$ and $B=\frac12$.

2025 HCI P1 Q9

2025 HCI P1 Q9

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