Category: Integration

Question Number 123552 by Lordose last updated on 26/Nov/20 $${\int }_0^{\frac{\pi }{4}}{\tan }^{\mathrm{n}}\left(\mathrm{x}\right)\mathrm{dx}$$ Answered by Adeleke last updated on 26/Nov/20 Answered by TANMAY…

Question Number 189066 by cortano12 last updated on 11/Mar/23 $$\mathrm{Given}\mathrm{f}\left(\mathrm{x}\right)+\underset{0}{\stackrel{1}{\int }}{(\mathrm{x}+\mathrm{y})}^2\mathrm{f}\left(\mathrm{y}\right)\mathrm{dy}={2\mathrm{x}}^2-3\mathrm{x}+1$$$$\mathrm{find}\mathrm{f}\left(\mathrm{x}\right).$$ Answered by horsebrand11 last updated on 11/Mar/23…

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}}…