Question and Answers Forum

All Questions      Topic List

Integration Questions

Previous in All Question      Next in All Question      

Previous in Integration      Next in Integration      

Question Number 184514 by BOYQOBILOV last updated on 08/Jan/23

Answered by SEKRET last updated on 19/Jan/23

t = x+(√(x^2 +1)) /_0 ^( 1) →/_1 ^( 1+(√2)) dt= 1+(x/( (√(x^2 +1)))) dx= ((x+(√(x^2 +1)))/( (√(x^2 +1)))) dx ∫_1 ^( 1+(√2)) ((√t)/( (√(x^2 +1)))) ∙ ((√(x^2 +1))/t) dt= ∫_1 ^(1+(√2)) (1/( (√t))) dt= 2(√t) ∣_1 ^(1+(√2)) =2∙((√(1+(√2) )) −1) ABDULAZIZ ABDUVALIYEV

$$\:\:\:\boldsymbol{\mathrm{t}}\:=\:\boldsymbol{\mathrm{x}}+\sqrt{\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\mathrm{1}}\:\:\:\:\:\:\:\:\:/_{\mathrm{0}} ^{\:\:\:\mathrm{1}} \rightarrow/_{\mathrm{1}} ^{\:\:\mathrm{1}+\sqrt{\mathrm{2}}} \\ $$$$\:\:\:\boldsymbol{\mathrm{dt}}=\:\mathrm{1}+\frac{\boldsymbol{\mathrm{x}}}{\:\sqrt{\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\mathrm{1}}}\:\boldsymbol{\mathrm{dx}}=\:\frac{\boldsymbol{\mathrm{x}}+\sqrt{\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\mathrm{1}}}{\:\sqrt{\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\mathrm{1}}}\:\boldsymbol{\mathrm{dx}} \\ $$$$\:\:\:\int_{\mathrm{1}} ^{\:\:\mathrm{1}+\sqrt{\mathrm{2}}} \frac{\sqrt{\boldsymbol{\mathrm{t}}}}{\:\sqrt{\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\mathrm{1}}}\:\centerdot\:\frac{\sqrt{\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\mathrm{1}}}{\boldsymbol{\mathrm{t}}}\:\boldsymbol{\mathrm{dt}}= \\ $$$$\:\:\int_{\mathrm{1}} ^{\mathrm{1}+\sqrt{\mathrm{2}}} \frac{\mathrm{1}}{\:\sqrt{\boldsymbol{\mathrm{t}}}}\:\boldsymbol{\mathrm{dt}}=\:\:\mathrm{2}\sqrt{\boldsymbol{\mathrm{t}}}\:\:\:\mid_{\mathrm{1}} ^{\mathrm{1}+\sqrt{\mathrm{2}}} =\mathrm{2}\centerdot\left(\sqrt{\mathrm{1}+\sqrt{\mathrm{2}}\:}\:−\mathrm{1}\right) \\ $$$$\:\boldsymbol{{ABDULAZIZ}}\:\:\:\boldsymbol{{ABDUVALIYEV}} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com