Menu Close

Category: Integration

E-pi-0-a-2-sin-2-a-2-x-2-2ax-cos-d-If-a-gt-x-show-that-E-a-2-x-

Question Number 168872 by MikeH last updated on 20/Apr/22 $${E}=\underset{\mathrm{0}} {\int}^{\pi} \left[\frac{{a}^{\mathrm{2}} \sigma\:\mathrm{sin}\:\theta}{\mathrm{2}\epsilon\sqrt{{a}^{\mathrm{2}} −{x}^{\mathrm{2}} −\mathrm{2}{ax}\:\mathrm{cos}\theta}}\right]{d}\theta \\ $$$$\mathrm{If}\:{a}>{x}\:\mathrm{show}\:\mathrm{that}\:{E}\:=\:\frac{{a}^{\mathrm{2}} \sigma}{\epsilon{x}} \\ $$ Commented by Tinku Tara last…

Question-168857

Question Number 168857 by Sotoberry last updated on 19/Apr/22 Answered by MJS_new last updated on 20/Apr/22 $$\int\frac{\mathrm{1}}{{x}^{\mathrm{3}} }\sqrt{\frac{{x}^{\mathrm{2}} −\mathrm{1}}{{x}+\mathrm{1}}}{dx}=\int\frac{\sqrt{{x}−\mathrm{1}}}{{x}^{\mathrm{3}} }{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\sqrt{{x}−\mathrm{1}}\:\rightarrow\:{dx}=\mathrm{2}\sqrt{{x}−\mathrm{1}}{dt}\right] \\ $$$$=\mathrm{2}\int\frac{{t}^{\mathrm{2}} }{\left({t}^{\mathrm{2}}…

Find-the-shortest-distance-between-the-curves-9x-2-9y-2-30y-16-0-and-y-2-x-3-

Question Number 37777 by rahul 19 last updated on 17/Jun/18 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{shortest}\:\mathrm{distance}\:\mathrm{between} \\ $$$$\mathrm{the}\:\mathrm{curves}\:\mathrm{9}{x}^{\mathrm{2}} +\mathrm{9}{y}^{\mathrm{2}} −\mathrm{30}{y}+\mathrm{16}=\mathrm{0}\:{and} \\ $$$${y}^{\mathrm{2}} ={x}^{\mathrm{3}} \:. \\ $$ Answered by MJS last…