Menu Close

Category: Integration

nice-calculus-prove-0-1-1-1-ln-2-x-dx-0-sin-x-1-x-dx-

Question Number 136497 by mnjuly1970 last updated on 22/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:……{nice}\:\:\:\:{calculus}….. \\ $$$$\:\:\:\:{prove}::\:\: \\ $$$$\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\mathrm{1}}{\mathrm{1}+{ln}^{\mathrm{2}} \left({x}\right)}{dx}=\int_{\mathrm{0}\:} ^{\:\infty} \frac{{sin}\left({x}\right)}{\mathrm{1}+{x}}{dx} \\ $$$$ \\ $$ Commented by…

0-7-2-x-1-2x-1-1-3-dx-

Question Number 5422 by love math last updated on 14/May/16 $$\int_{\mathrm{0}} ^{\frac{\mathrm{7}}{\mathrm{2}}} \left({x}+\mathrm{1}\right)\left(\mathrm{2}{x}+\mathrm{1}\right)^{\frac{\mathrm{1}}{\mathrm{3}}} {dx} \\ $$ Answered by nchejane last updated on 14/May/16 $$=\left[\frac{\mathrm{3}}{\mathrm{8}}\left({x}+\mathrm{1}\right)\left(\mathrm{2}{x}+\mathrm{1}\right)^{\frac{\mathrm{4}}{\mathrm{3}}} \right]_{\mathrm{0}}…

1-3-ln-3x-2-dx-

Question Number 5425 by love math last updated on 14/May/16 $$\int_{\mathrm{1}} ^{\mathrm{3}} {ln}\left(\mathrm{3}{x}−\mathrm{2}\right){dx} \\ $$ Answered by nchejane last updated on 14/May/16 $$\left[{xln}\left(\mathrm{3}{x}−\mathrm{2}\right)\right]_{\mathrm{1}} ^{\mathrm{3}} −\mathrm{3}\int_{\mathrm{1}}…

0-50pi-3-sinx-dx-

Question Number 136481 by BHOOPENDRA last updated on 22/Mar/21 $$\int_{\mathrm{0}} ^{\frac{\mathrm{50}\pi}{\mathrm{3}}} \mid{sinx}\mid{dx} \\ $$ Answered by MJS_new last updated on 22/Mar/21 $$\underset{\mathrm{0}} {\overset{\mathrm{50}\pi/\mathrm{3}} {\int}}\mid\mathrm{sin}\:{x}\mid{dx}=\mathrm{33}\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}}…