Question Number 174406 by Best1 last updated on 31/Jul/22
Answered by alephzero last updated on 31/Jul/22
$$\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{4}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }+\mathrm{2}\right)\:\mathrm{d}{x}\:= \\ $$$$\mathrm{4}\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{1}−{x}^{\mathrm{2}} \:}\mathrm{d}{x}\:+\int_{\mathrm{0}} ^{\mathrm{1}} \:\mathrm{2}\:\mathrm{d}{x}\:=\:\pi\:+\:\mathrm{2} \\ $$$$\mathrm{A}. \\ $$