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Category: Integration

0-1-ln-x-1-x-2-x-dx-

Question Number 140961 by iloveisrael last updated on 14/May/21 $$\:\underset{\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\:\:\frac{\mathrm{ln}\:\left({x}+\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\right)}{{x}}\:{dx}\:=?\: \\ $$ Answered by qaz last updated on 14/May/21 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{ln}\left({x}+\sqrt{\mathrm{1}−{x}^{\mathrm{2}}…

nice-calculus-if-n-0-cos-npi-2n-then-Re-

Question Number 140966 by mnjuly1970 last updated on 14/May/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…….{nice}……{calculus}….. \\ $$$$\:\:\:\:\:{if}\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\sqrt{{cos}\:\left({n}\pi\right)}\:}{\left(\mathrm{2}{n}\right)!!}\:=\:\omega \\ $$$$\:\:\:\:\:\:\:{then}\:\:\:{Re}\left(\omega\right):=?? \\ $$ Answered by Dwaipayan Shikari last updated on…

advanced-calculus-prove-that-sin-4-x-cos-4-x-x-2-dx-pi-16-m-n-

Question Number 140956 by mnjuly1970 last updated on 14/May/21 $$\:\:\:\:\:\:\:\:\:\:…..{advanced}……{calculus}….. \\ $$$$\:\:\:\:\:{prove}\:{that}: \\ $$$$\:\:\boldsymbol{\phi}:=\:\int_{−\infty} ^{\:\infty} \frac{{sin}^{\mathrm{4}} \left({x}\right).{cos}^{\mathrm{4}} \left({x}\right)}{{x}^{\mathrm{2}} }{dx}=\frac{\pi}{\mathrm{16}} \\ $$$$\:\:{m}.{n} \\ $$ Answered by…

0-pi-dx-2-cos-x-

Question Number 140930 by bramlexs22 last updated on 14/May/21 $$\underset{\mathrm{0}} {\overset{\pi} {\int}}\:\frac{\mathrm{dx}}{\:\sqrt{\mathrm{2}}\:−\mathrm{cos}\:\mathrm{x}} \\ $$ Answered by Dwaipayan Shikari last updated on 14/May/21 $$\mathrm{2}\int_{\mathrm{0}} ^{\infty} \frac{{dt}}{\:\sqrt{\mathrm{2}}−\frac{\mathrm{1}−{t}^{\mathrm{2}}…