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 78700 by abdomathmax last updated on 20/Jan/20

calculate ∫∫_D ((∣x−2∣)/y)dxdy with D={(x,y)∈R^2 /0≤x≤3 and 1≤y≤e}

calculate∫∫D∣x−2∣ydxdywithD={(x,y)∈R2/0⩽x⩽3and1⩽y⩽e}

Commented by john santu last updated on 20/Jan/20

= ∫_1 ^( e) ∫_0 ^( 3) (((∣x−2∣)/y) )dx dy = ∫_(1 ) ^( e) (((2x−(1/2)x^2 )∣_0 ^2 +((1/2)x^2 −2x)∣_2 ^3 )/y) dy = ∫_1 ^( e) (( 2+(1/2))/y) dy = (5/2)(ln y) ∣_1 ^e = (5/2)

=∫1e∫03(∣x−2∣y)dxdy=∫1e(2x−12x2)∣02+(12x2−2x)∣23ydy=∫1e2+12ydy=52(lny)∣1e=52

Terms of Service

Privacy Policy

Contact: info@tinkutara.com