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Question Number 51 by surabhi last updated on 25/Jan/15
Evaluate ∫_0 ^(π/2) xcos x dx
$$\mathrm{Evaluate}\:\int_{\mathrm{0}} ^{\pi/\mathrm{2}} {x}\mathrm{cos}\:{x}\:{dx} \\ $$
Answered by surabhi last updated on 04/Nov/14
∫_0 ^(π/2) xcos x dx=[xsin x]_0 ^(π/2) −∫_0 ^(π/2) 1∙sin x dx =(π/2)+[cos x]_0 ^(π/2) =(π/2)−1
$$\int_{\mathrm{0}} ^{\pi/\mathrm{2}} {x}\mathrm{cos}\:{x}\:{dx}=\left[{x}\mathrm{sin}\:{x}\right]_{\mathrm{0}} ^{\pi/\mathrm{2}} −\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \mathrm{1}\centerdot\mathrm{sin}\:{x}\:{dx} \\ $$$$=\frac{\pi}{\mathrm{2}}+\left[\mathrm{cos}\:{x}\right]_{\mathrm{0}} ^{\pi/\mathrm{2}} =\frac{\pi}{\mathrm{2}}−\mathrm{1}\: \\ $$

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