Question Number 199753 by sonukgindia last updated on 08/Nov/23
Answered by MM42 last updated on 09/Nov/23
$${let}\:\::\:\:{f}={xsinx}+{cosx}\:\:\&\:\:{g}={xcosx}+{sinx} \\ $$$${f}={g}\:\:\overset{\mathrm{0}\leqslant{x}\leqslant\mathrm{1}} {\Rightarrow}\:{x}=\mathrm{1}\:,\frac{\pi}{\mathrm{4}} \\ $$$$\Rightarrow{s}=\mid\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \left({f}−{g}\right){dx}\mid+\mid\int_{\frac{\pi}{\mathrm{4}}} ^{\mathrm{1}} \left({f}−{g}\right){dx}\:\mid \\ $$$$=\mathrm{2}\sqrt{\mathrm{2}}−\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}\pi+{cos}\mathrm{1}−{sin}\mathrm{1}\:\:\checkmark \\ $$$$ \\ $$