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Category: Integration

Question-179042

Question Number 179042 by mnjuly1970 last updated on 23/Oct/22 Answered by Ar Brandon last updated on 23/Oct/22 $${I}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{cos}^{\mathrm{2}} {x}}{\mathrm{sin}^{\mathrm{4}} {x}+\mathrm{cos}^{\mathrm{2}} {x}}{dx}=\int_{\mathrm{0}} ^{\infty} \frac{{dt}}{{t}^{\mathrm{4}}…

A-particle-moves-in-a-linear-scare-such-that-acceleration-after-t-seconds-is-a-ms-2-where-a-2t-2-t-If-its-initial-velocity-was-3ms-1-find-an-expression-for-S-the-distance-in-meters-travele

Question Number 47967 by Rio Michael last updated on 17/Nov/18 $${A}\:{particle}\:{moves}\:{in}\:{a}\:{linear}\:{scare}\:{such}\:{that}\:{acceleration} \\ $$$${after}\:{t}\:{seconds}\:{is}\:{a}\:{ms}^{−\mathrm{2}} \:{where}\:{a}=\:\mathrm{2}{t}^{\mathrm{2}} +\:{t}.{If}\:{its}\:{initial}\: \\ $$$${velocity}\:{was}\:\mathrm{3}{ms}^{−\mathrm{1}} \:{find}\:{an}\:{expression}\:{for}\:{S},{the}\:{distance}\:{in}\:{meters} \\ $$$${traveled}\:{from}\:{start}\:{t}\:{seconds}. \\ $$ Answered by ajfour…

Question-47915

Question Number 47915 by behi83417@gmail.com last updated on 16/Nov/18 Answered by MJS last updated on 16/Nov/18 $${f}\left({x}\right)\:\mathrm{is}\:\mathrm{kind}\:\mathrm{of}\:\mathrm{a}\:\mathrm{parabola}.\:\mathrm{I}\:\mathrm{don}'\mathrm{t}\:\mathrm{think}\:\mathrm{we} \\ $$$$\mathrm{can}\:\mathrm{find}\:{f}^{−\mathrm{1}} \left({x}\right)\:\mathrm{but}\:\mathrm{of}\:\mathrm{course}\:\mathrm{we}\:\mathrm{can}\:\mathrm{approximately} \\ $$$$\mathrm{calculate}\:\mathrm{the}\:\mathrm{area}.\:\mathrm{area}\:\mathrm{between}\:{f}\:\mathrm{and}\:{f}^{−\mathrm{1}} = \\ $$$$=\mathrm{2}×\mathrm{area}\:\mathrm{between}\:{f}\:\mathrm{and}\:{y}={x}…

let-f-x-x-1-x-and-g-x-x-1-x-find-f-x-g-x-dx-and-f-x-dx-g-x-dx-

Question Number 47851 by maxmathsup by imad last updated on 15/Nov/18 $${let}\:\:{f}\left({x}\right)={x}+\mathrm{1}+\sqrt{{x}}\:{and}\:{g}\left({x}\right)={x}+\mathrm{1}−\sqrt{{x}} \\ $$$${find}\:\int\:\frac{{f}\left({x}\right)}{{g}\left({x}\right)}{dx}\:\:{and}\:\:\frac{\int{f}\left({x}\right){dx}}{\int{g}\left({x}\right){dx}}\:. \\ $$ Commented by maxmathsup by imad last updated on 16/Nov/18…