Menu Close

Category: None

v-pi-0-2-x-2-dx-

Question Number 91497 by kikomssn@gmail.com last updated on 01/May/20 $${v}=\pi\int_{\mathrm{0}} ^{\mathrm{2}} {x}^{\mathrm{2}} {dx} \\ $$ Commented by jagoll last updated on 01/May/20 $$\left.=\:\frac{\pi{x}^{\mathrm{3}} }{\mathrm{3}}\:\right]_{\mathrm{0}} ^{\mathrm{2}}…

If-xcos-ycos-zcos-0-xsin-ysin-zsin-0-and-xsec-ysec-zsec-0-then-prove-that-x-2-y-2-z-2-2-4x-2-y-2-

Question Number 157031 by PRITHWISH SEN 2 last updated on 18/Oct/21 $$\mathrm{If}\:\:\mathrm{xcos}\:\theta+\mathrm{ycos}\:\emptyset+\mathrm{zcos}\:\psi=\mathrm{0}, \\ $$$$\:\:\:\:\:\:\mathrm{xsin}\:\theta+\mathrm{ysin}\:\emptyset+\mathrm{zsin}\:\psi=\mathrm{0} \\ $$$$\mathrm{and}\:\mathrm{xsec}\:\theta+\mathrm{ysec}\:\emptyset+\mathrm{zsec}\:\psi=\mathrm{0} \\ $$$$\mathrm{then}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\:\:\:\:\left(\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} −\mathrm{z}^{\mathrm{2}} \right)^{\mathrm{2}} =\:\mathrm{4x}^{\mathrm{2}} \mathrm{y}^{\mathrm{2}}…

Question-91465

Question Number 91465 by Zainal Arifin last updated on 30/Apr/20 Commented by Prithwish Sen 1 last updated on 01/May/20 $$\mathrm{8}.\frac{\mathrm{2}.\mathrm{sin}\frac{\mathrm{2}\pi}{\mathrm{15}}.\mathrm{cos}\frac{\mathrm{2}\pi}{\mathrm{15}}}{\mathrm{sin}\frac{\mathrm{2}\pi}{\mathrm{15}}}\:.\mathrm{cos}\frac{\mathrm{4}\pi}{\mathrm{15}}\mathrm{cos}\frac{\mathrm{8}\pi}{\mathrm{15}}\mathrm{cos}\frac{\mathrm{14}\pi}{\mathrm{15}} \\ $$$$=\mathrm{2}.\frac{\mathrm{sin}\frac{\mathrm{16}\pi}{\mathrm{15}}}{\mathrm{sin}\frac{\mathrm{2}\pi}{\mathrm{15}}}.\mathrm{cos}\frac{\mathrm{14}\pi}{\mathrm{15}}=\mathrm{2}.\frac{\mathrm{sin}\left(\pi+\frac{\pi}{\mathrm{15}}\right)}{\mathrm{sin}\frac{\mathrm{2}\pi}{\mathrm{15}}}.\mathrm{cos}\left(\pi−\frac{\pi}{\mathrm{15}}\right) \\ $$$$=\mathrm{2}.\frac{\mathrm{sin}\frac{\pi}{\mathrm{15}}}{\mathrm{2}.\mathrm{sin}\frac{\pi}{\mathrm{15}}.\mathrm{cos}\frac{\pi}{\mathrm{15}}}\:.\:\mathrm{cos}\frac{\pi}{\mathrm{15}}\:=\:\mathrm{1}\: \\…

x-3-4-5-

Question Number 25924 by vipinrana4542@gmail.com last updated on 16/Dec/17 $${x}+\mathrm{3}+\mathrm{4}=\mathrm{5} \\ $$ Answered by Rasheed.Sindhi last updated on 16/Dec/17 $$\mathrm{x}+\mathrm{7}=\mathrm{5} \\ $$$$\mathrm{x}=\mathrm{5}−\mathrm{7} \\ $$$$\mathrm{x}=−\mathrm{2} \\…

Question-156933

Question Number 156933 by CAIMAN last updated on 17/Oct/21 Answered by mindispower last updated on 17/Oct/21 $$\frac{\mathrm{1}}{{t}}={x} \\ $$$$\int_{\frac{\mathrm{1}}{\mathrm{2}}} ^{\frac{\mathrm{1}}{\mathrm{3}}} \frac{{ln}\left({x}\right)}{{x}\left(\mathrm{1}+{x}\right)}{dx}=\int\frac{{ln}\left({x}\right)}{{x}}−\frac{{ln}\left({x}\right)}{\mathrm{1}+{x}}{dx} \\ $$$$=\frac{{ln}^{\mathrm{2}} \left({x}\right)}{\mathrm{2}}−{ln}\left({x}\right){ln}\left(\mathrm{1}+{x}\right)+\int\frac{{ln}\left(\mathrm{1}+{x}\right)}{{x}}{dx} \\…