<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Find $\int{\sin x\cos 3x\,\,\mathrm{d}x}$.</span></div><p style="text-align: right;">[2]</p></li><li><div class="list-item-content"><span class="list-item-text">Find $\int{\frac{x-1}{\sqrt{1+2x-{{x}^{2}}}}}\,\mathrm{d}x$. Find the greatest integer value of $b$ such that $\int_{0}^{b}{\frac{x-1}{\sqrt{1+2x-{{x}^{2}}}}}\,\mathrm{d}x$ is defined.</span></div><p style="text-align: right;">[5]</p></li><li><div class="list-item-content"><span class="list-item-text">Find $\int{x\cos x\,\,\mathrm{d}x}$. Hence find the exact value of $\int_{0}^{2\pi }{x\left| \cos x \right|\mathrm{d}x}$.</span></div><p style="text-align: right;">[5]</p></li></ol>

Find $\displaystyle\displaystyle \int{\sin x\cos 3x\,\,\mathrm{d}x}$.

Find $\displaystyle\displaystyle \int{\frac{x-1}{\sqrt{1+2x-{{x}^{2}}}}}\,\mathrm{d}x$. Find the greatest integer value of $b$ such that $\displaystyle\displaystyle \int_{0}^{b}{\frac{x-1}{\sqrt{1+2x-{{x}^{2}}}}}\,\mathrm{d}x$ is defined.

Find $\displaystyle\displaystyle \int{x\cos x\,\,\mathrm{d}x}$. Hence find the exact value of $\displaystyle\displaystyle \int_{0}^{2\pi }{x\left| \cos x \right|\mathrm{d}x}$.

2019 TJC Promo Q5

2019 TJC Promo Q5

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