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Category: Integration

2x-3-1-x-4-x-dx-

Question Number 144792 by imjagoll last updated on 29/Jun/21 $$\:\int\:\frac{\mathrm{2x}^{\mathrm{3}} −\mathrm{1}}{\mathrm{x}^{\mathrm{4}} +\mathrm{x}}\:\mathrm{dx}\:? \\ $$ Answered by liberty last updated on 29/Jun/21 $$\:\Omega=\int\:\frac{\mathrm{2x}^{\mathrm{3}} −\mathrm{1}}{\mathrm{x}^{\mathrm{4}} +\mathrm{x}}\:\mathrm{dx}\:=\:\int\:\frac{\mathrm{2x}−\mathrm{x}^{−\mathrm{2}} }{\mathrm{x}^{\mathrm{2}}…

Question-144788

Question Number 144788 by nonh1 last updated on 29/Jun/21 Answered by gsk2684 last updated on 30/Jun/21 $$\underset{\mathrm{x}=\mathrm{0}} {\overset{\mathrm{1}} {\int}}\left(\underset{\mathrm{y}=−\mathrm{3}} {\overset{\mathrm{3}} {\int}}\left(\mathrm{4}−\mathrm{y}^{\mathrm{2}} \right)\mathrm{dy}\right)\:\mathrm{dx} \\ $$$$\underset{\mathrm{0}} {\overset{\mathrm{1}}…

Q-Calculus-If-n-0-1-x-2n-1-x-2-dx-then-find-the-value-of-

Question Number 144787 by mnjuly1970 last updated on 29/Jun/21 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{Q}\:::\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:#\:\mathrm{Calculus}\:# \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{If}\::\:\:\:\:\:\:\:\:\boldsymbol{\phi}\:\left(\:{n}\:\right)\::\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:{x}^{\:\mathrm{2}{n}} }{\mathrm{1}\:+\:{x}^{\:\mathrm{2}} }\:\mathrm{d}{x}\: \\ $$$$\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{then}\:\:\mathrm{find}\:\:\mathrm{the}\:\:\mathrm{value}\:\mathrm{of}\::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\…

Assuming-no-air-resistance-and-angle-of-projection-pi-4-find-the-ratio-of-the-length-of-trajectory-L-of-a-projectile-motion-by-the-time-it-hits-the-ground-to-its-horizontal-range-R-on-ground

Question Number 13705 by ajfour last updated on 22/May/17 $${Assuming}\:{no}\:{air}\:{resistance}, \\ $$$${and}\:{angle}\:{of}\:{projection}\:\alpha=\frac{\pi}{\mathrm{4}}\:, \\ $$$${find}\:{the}\:{ratio}\:{of}\:{the}\:{length}\:{of} \\ $$$${trajectory}\:\boldsymbol{{L}}\:{of}\:{a}\:{projectile}\:{motion}\: \\ $$$$\left({by}\:{the}\:{time}\:{it}\:{hits}\:{the}\:{ground}\right) \\ $$$${to}\:{its}\:{horizontal}\:{range}\:\boldsymbol{{R}}\:{on}\: \\ $$$${ground}.\:\:\:\:\:\:\frac{\boldsymbol{{L}}}{\boldsymbol{{R}}}=? \\ $$ Commented…

A-region-is-enclosed-by-curves-x-2-4y-x-2-4y-x-4-amp-x-4-V-1-is-the-volume-of-the-solid-obtained-by-rotating-the-above-region-round-the-y-axis-Another-regions-consists-of-points-x-y-satisf

Question Number 144771 by imjagoll last updated on 29/Jun/21 $$\mathrm{A}\:\mathrm{region}\:\mathrm{is}\:\mathrm{enclosed}\:\mathrm{by}\:\mathrm{curves} \\ $$$$\mathrm{x}^{\mathrm{2}} =\mathrm{4y},\:\mathrm{x}^{\mathrm{2}} =−\mathrm{4y},\:\mathrm{x}=\mathrm{4}\:\&\:\mathrm{x}=−\mathrm{4} \\ $$$$\mathrm{V}_{\mathrm{1}} \mathrm{is}\:\mathrm{the}\:\mathrm{volume}\:\mathrm{of}\:\mathrm{the}\:\mathrm{solid}\:\mathrm{obtained} \\ $$$$\mathrm{by}\:\mathrm{rotating}\:\mathrm{the}\:\mathrm{above}\:\mathrm{region}\:\mathrm{round} \\ $$$$\mathrm{the}\:\mathrm{y}−\mathrm{axis}.\:\:\mathrm{Another}\:\mathrm{regions} \\ $$$$\mathrm{consists}\:\mathrm{of}\:\mathrm{points}\:\left(\mathrm{x},\mathrm{y}\right)\:\mathrm{satisfying} \\ $$$$\mathrm{x}^{\mathrm{2}}…

Question-144764

Question Number 144764 by nonh1 last updated on 29/Jun/21 Answered by liberty last updated on 29/Jun/21 $$\int_{\mathrm{0}} ^{\:\sqrt{\mathrm{ln}\:\mathrm{2}}} \int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\mathrm{1}}{\mathrm{2}}\mathrm{xe}^{\mathrm{x}^{\mathrm{2}} } \:\left(\frac{\mathrm{d}\left(\mathrm{1}+\mathrm{y}^{\mathrm{2}} \right)}{\mathrm{1}+\mathrm{y}^{\mathrm{2}} }\right)\mathrm{dx}…