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 198948 by ArifinTanjung last updated on 26/Oct/23

∫_1 ^3 ((x−2)/(x^2 −4x)) dx= ....

∫13x−2x2−4xdx=....

Answered by ajfour last updated on 26/Oct/23

I=(1/2)∫_(−1) ^( 1) ((2tdt)/(t^2 −4))=0 (odd function) ∫_(−a) ^( a) f(x)dx=0 if f(−x)=−f(x)

I=12∫−112tdtt2−4=0(oddfunction)∫−aaf(x)dx=0iff(−x)=−f(x)

Answered by mr W last updated on 26/Oct/23

∫_1 ^3 ((x−2)/(x^2 −4x))dx =∫_1 ^2 ((x−2)/(x^2 −4x))dx+∫_2 ^3 ((x−2)/(x^2 −4x))dx =∫_1 ^2 ((x−2)/(x^2 −4x))dx+∫_2 ^1 ((4−t−2)/((4−t)(4−t−4)))d(4−t) =∫_1 ^2 ((x−2)/(x^2 −4x))dx+∫_2 ^1 ((t−2)/(t^2 −4t))dt =∫_1 ^2 ((x−2)/(x^2 −4x))dx−∫_1 ^2 ((x−2)/(x^2 −4x))dx =0

∫13x−2x2−4xdx=∫12x−2x2−4xdx+∫23x−2x2−4xdx=∫12x−2x2−4xdx+∫214−t−2(4−t)(4−t−4)d(4−t)=∫12x−2x2−4xdx+∫21t−2t2−4tdt=∫12x−2x2−4xdx−∫12x−2x2−4xdx=0

Terms of Service

Privacy Policy

Contact: info@tinkutara.com