Category: Integration

Question Number 57992 by Tinkutara last updated on 15/Apr/19 Answered by MJS last updated on 16/Apr/19 $$\underset{1}{\stackrel{c}{\int }}(-x^5+8x^2)dx=\frac{16}{3}$$$$−\frac{\mathrm{1}}{\mathrm{6}}{c}^{\mathrm{6}} +\frac{\mathrm{8}}{\mathrm{3}}{c}^{\mathrm{3}} −\frac{\mathrm{5}}{\mathrm{2}}=\frac{\mathrm{16}}{\mathrm{3}}…

Question Number 189057 by neinhaltsieger369 last updated on 11/Mar/23 $$$$$$\mathrm{Help}!$$$$$$$$\mathrm{Evaluate}\mathrm{the}\mathrm{following}\mathrm{integral}\mathrm{usings}\mathrm{Green}\mathrm{theorem}:$$$$$$$$\oint 4\mathrm{xy}d\mathrm{x}+{\mathrm{x}}^{2}d\mathrm{y}$$$$$$$$\:\mathrm{Where}\:\:{C}\:\:\mathrm{is}\:\:\mathrm{the}\:\:\mathrm{square}\:\:\mathrm{of}\:\:\mathrm{vertices}\:\:\left(\mathrm{0},\mathrm{0}\right),\:\left(\mathrm{0},\mathrm{2}\right),\:\left(\mathrm{2},\mathrm{0}\right)\:\:\mathrm{and}\:\:\left(\mathrm{2},\mathrm{2}\right).…

Question Number 123494 by bemath last updated on 25/Nov/20 $$\int \frac{x-1}{(x+1)\sqrt{x^3+x^2+x}}dx?$$ Answered by bramlexs22 last updated on 26/Nov/20 $$\:{I}\left({x}\right)=\int\:\frac{{x}^{\mathrm{2}} −\mathrm{1}}{\left({x}+\mathrm{1}\right)^{\mathrm{2}} \sqrt{{x}^{\mathrm{3}} +{x}^{\mathrm{2}}…

Question Number 57948 by maxmathsup by imad last updated on 14/Apr/19 $$letA\left(\xi \right)={\int }_{\xi }^{{\xi }^2}\frac{arctan(1+\xi t)-\frac{\pi }{4}}{\sqrt{2+\xi t}-\sqrt{2-\xi t}}dt$$$$find{lim}_{\xi \to 0}A\left(\xi \right).$$$$$$ Terms of Service…

Question Number 123456 by mnjuly1970 last updated on 25/Nov/20 $$\dots advancedcalculus\dots$$$$prove::$$$$\varphi =\underset{n=1}{\sum ^{\mathrm{\infty }}}\left(\frac{{\mathrm{H}}_n}{n^3}\right)\stackrel{???}{=}\frac{{\pi }^4}{72}$$$$note:{\mathrm{H}}_n=1+\frac{1}{2}+\dots +\frac{1}{n}$$…