Menu Close

Category: Integration

What-is-1-3-1-x-4-dx-equal-to-a-232-5-b-116-5-c-116-5-d-232-5-

Question Number 12303 by Gaurav3651 last updated on 18/Apr/17 $${What}\:{is}\underset{\mathrm{1}} {\overset{\mathrm{3}} {\int}}\mid\mathrm{1}−{x}^{\mathrm{4}} \:\mid{dx}\:{equal}\:{to}? \\ $$$$\left({a}\right)\:\:−\mathrm{232}/\mathrm{5} \\ $$$$\left({b}\right)\:\:−\mathrm{116}/\mathrm{5} \\ $$$$\left({c}\right)\:\:\:\mathrm{116}/\mathrm{5} \\ $$$$\left({d}\right)\:\:\:\mathrm{232}/\mathrm{5} \\ $$ Answered by…

Let-f-x-be-a-function-such-that-f-1-x-x-3-f-x-0-What-is-1-1-f-x-dx-equal-to-a-2f-1-b-0-c-2f-1-d-4f-1-

Question Number 12302 by Gaurav3651 last updated on 18/Apr/17 $${Let}\:{f}\left({x}\right)\:{be}\:{a}\:{function}\:{such}\:{that} \\ $$$${f}'\left(\mathrm{1}/{x}\right)+{x}^{\mathrm{3}} {f}'\left({x}\right)=\mathrm{0}. \\ $$$${What}\:{is}\:\underset{−\mathrm{1}} {\overset{\mathrm{1}} {\int}}{f}\left({x}\right){dx}\:{equal}\:{to}? \\ $$$$\left({a}\right)\:\:\mathrm{2}{f}\left(\mathrm{1}\right) \\ $$$$\left({b}\right)\:\:\mathrm{0} \\ $$$$\left({c}\right)\:\:\mathrm{2}{f}\left(−\mathrm{1}\right) \\ $$$$\left({d}\right)\:\:\mathrm{4}{f}\left(\mathrm{1}\right)…

0-1-1-log-x-dx-

Question Number 77790 by aliesam last updated on 10/Jan/20 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}}{\:\sqrt{−{log}\left({x}\right)}}\:{dx} \\ $$ Answered by MJS last updated on 10/Jan/20 $$\int\frac{{dx}}{\:\sqrt{−\mathrm{ln}\:{x}}}= \\ $$$$\:\:\:\:\:\left[{t}=\sqrt{−\mathrm{ln}\:{x}}\:\rightarrow\:{dx}=−\mathrm{2}{x}\sqrt{−\mathrm{ln}\:{x}}{dt}\right] \\…

0-sin-4-x-x-4-dx-pi-3-

Question Number 143312 by Ar Brandon last updated on 12/Jun/21 $$\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{sin}^{\mathrm{4}} \mathrm{x}}{\mathrm{x}^{\mathrm{4}} }\mathrm{dx}=\frac{\pi}{\mathrm{3}} \\ $$ Answered by Olaf_Thorendsen last updated on 12/Jun/21 $$\mathrm{Let}\:{f}\left({x}\right)\:=\:\mathrm{1}\:\left(\mathrm{constant}\:\mathrm{function}\:\mathrm{unity}\right)…