calculate the double integral: 5xsin(x+y) dA R=[0,pi/3] x [0,pi/6] PLEASE HELP ME!!!?

NetherCraft 0

1 Answer

  • I’ll integrate with respect to x first:

    integral(y in [0, pi/6], x in [0, pi/3]) 5x sin(x+y) dx dy

    = integral(y in [0, pi/6]) -5x cos(x+y) + 5 sin(x+y) {x in [0, pi/3]} dy

    (via integration by parts)

    = 5 integral(y in [0, pi/6]) ((-pi/3) cos(pi/3 + y) + sin(pi/3 + y) – sin y) dy

    = 5 ((-pi/3) sin(pi/3 + y) – cos(pi/3 + y) + cos y) {for y in [0, pi/6]}

    = 5 [-pi/3 + sqrt(3)/2 + (pi/3) sqrt(3)/2 – 1/2] = 1.12864…

    (Verified on Wolfram Alpha.)

    I hope this helps!

Also Check This  How do i convert m2 to cm3?

Leave a Reply

Your email address will not be published. Required fields are marked *