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Author: Tinku Tara

f-x-2-x-2f-x-2-3x-2-9x-2-15x-then-what-is-the-value-of-f-10-

Question Number 23833 by Joel577 last updated on 07/Nov/17 $${f}\left({x}^{\mathrm{2}} \:+\:{x}\right)\:+\:\mathrm{2}{f}\left({x}^{\mathrm{2}} \:−\:\mathrm{3}{x}\:+\:\mathrm{2}\right)\:=\:\mathrm{9}{x}^{\mathrm{2}} \:−\:\mathrm{15}{x} \\ $$$$\mathrm{then}\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{f}\left(\mathrm{10}\right)\:? \\ $$ Commented by prakash jain last updated on 07/Nov/17…

sin-101x-sin-99-xdx-

Question Number 23830 by anunil1234 last updated on 07/Nov/17 $$\int\mathrm{sin}\left(\mathrm{101x}\right)\mathrm{sin}^{\mathrm{99}} \mathrm{xdx} \\ $$ Commented by prakash jain last updated on 07/Nov/17 $$\mathrm{sin}\:\left(\mathrm{100}{x}+{x}\right)\mathrm{sin}^{\mathrm{99}} {x} \\ $$$$=\mathrm{sin}\:\left(\mathrm{100}{x}\right)\mathrm{cos}\:{x}\mathrm{sin}^{\mathrm{99}}…

1-x-x-1-3-

Question Number 89362 by cindiaulia last updated on 17/Apr/20 $$\int\frac{\mathrm{1}}{\:\sqrt{\mathrm{x}}\left(\sqrt{\mathrm{x}}+\mathrm{1}\right)^{\mathrm{3}} } \\ $$ Commented by jagoll last updated on 17/Apr/20 $${u}\:=\:\mathrm{1}+\sqrt{{x}}\:\Rightarrow\:{du}\:=\:\frac{{dx}}{\mathrm{2}\sqrt{{x}}}\: \\ $$$$\int\:\frac{\mathrm{2}\:{du}}{{u}^{\mathrm{3}} }\:=\:\int\:\mathrm{2}{u}^{−\mathrm{3}} \:{du}\:=\:−{u}^{−\mathrm{2}}…

find-the-following-please-S-k-1-n-1-k-k-1-k-2-

Question Number 154896 by maged last updated on 22/Sep/21 $${find}\:{the}\:{following}\:?{please} \\ $$$${S}=\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{k}\left({k}+\mathrm{1}\right)\left({k}+\mathrm{2}\right)} \\ $$ Commented by benhamimed last updated on 23/Sep/21 $$\Sigma\frac{\mathrm{1}}{{k}\left({k}+\mathrm{1}\right)\left({k}+\mathrm{2}\right)}=\Sigma\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{\mathrm{1}}{{k}}−\frac{\mathrm{2}}{{k}+\mathrm{1}}+\frac{\mathrm{1}}{{k}+\mathrm{2}}\right) \\…