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Category: Integration

sin-4-x-cos-4-xdx-

Question Number 9581 by dc630248@gmail.com last updated on 18/Dec/16 $$\int\mathrm{sin}^{\mathrm{4}} {x}.\mathrm{cos}^{\mathrm{4}} {xdx} \\ $$ Answered by mrW last updated on 18/Dec/16 $$\mathrm{sin}^{\mathrm{4}} {x}.\mathrm{cos}^{\mathrm{4}} {x}=\frac{\mathrm{1}}{\mathrm{16}}\left(\mathrm{2sinxcosx}\right)^{\mathrm{4}} =\frac{\mathrm{1}}{\mathrm{16}}\mathrm{sin}^{\mathrm{4}}…

show-by-integration-that-the-centroid-of-a-semi-circular-lamina-of-radius-a-from-the-centre-is-4a-3pi-

Question Number 75102 by Rio Michael last updated on 07/Dec/19 $$\mathrm{show}\:\mathrm{by}\:\mathrm{integration}\:\mathrm{that}\:\mathrm{the}\:\mathrm{centroid} \\ $$$$\mathrm{of}\:\mathrm{a}\:\mathrm{semi}−\mathrm{circular}\:\mathrm{lamina}\:\mathrm{of}\:\mathrm{radius}\:{a}\: \\ $$$$\mathrm{from}\:\mathrm{the}\:\mathrm{centre}\:\mathrm{is}\:\:\:\frac{\mathrm{4}{a}}{\mathrm{3}\pi}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

let-U-n-0-x-n-logx-x-2-1-2-dx-1-explicite-U-n-2-fond-nature-of-U-n-n-integr-natural-

Question Number 140639 by Mathspace last updated on 10/May/21 $${let}\:{U}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\frac{{x}^{{n}} {logx}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$$$\left.\mathrm{1}\right)\:{explicite}\:{U}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{fond}\:{nature}\:{of}\:\Sigma\:{U}_{{n}} \\ $$$$\left({n}\:{integr}\:{natural}\right) \\ $$ Answered…

the-function-f-is-defined-by-f-x-2-x-2-1-a-Express-f-into-partial-fraction-b-show-that-3-5-f-x-dx-ln-4-3-

Question Number 75098 by Rio Michael last updated on 07/Dec/19 $$\mathrm{the}\:\mathrm{function}\:\mathrm{f}\:\mathrm{is}\:\mathrm{defined}\:\mathrm{by}\:{f}\left({x}\right)\:=\:\frac{\mathrm{2}}{{x}^{\mathrm{2}} −\mathrm{1}} \\ $$$$\left.{a}\right)\:\mathrm{Express}\:\mathrm{f}\:\mathrm{into}\:\mathrm{partial}\:\mathrm{fraction} \\ $$$$\mathrm{b}.\mathrm{show}\:\mathrm{that}\:\int_{\mathrm{3}} ^{\mathrm{5}} {f}\left({x}\right)\:{dx}\:=\:{ln}\left(\frac{\mathrm{4}}{\mathrm{3}}\right) \\ $$ Answered by peter frank last…