maths help needed.?

Question

evaluate the following integrals

i) Integrate (y log y) dy

how do i do this, it's in a revision book but i cant remember ever doin it.

thanks

Answer 1

Ok, i don't know how much math you know but i prob Would say your entering 2nd year uni or earlier so you should (hopefully) know the method of integration by parts...

For this particular question use the substitution
U=ln(y) => dU=1/y dy and
dV=ydy => V=(y^2)/2

note: ^ the symbol for to the power to i.e y squared

Then use the standard integration by parts formula (which is really important-so learn it!)

int(UdV) = UV - int(VdU)

where i have denoted 'int' to be the integral
this gives

int(y.ln(y))dy = (1/2)(y^2)ln(y) - (1/4).y^2

you can always check by differentiating it back.

Any further questions just ask. Good luck

Answer 2

Use integration by parts. Take u = ln y, dv = ydy; then du = dy/y and v = (y^2)/2 and you find your integral is [(y^2)/2]*(ln y - 1/2) + C.