Question

integrate: (0 to 5) for y(sqrt(25 − (y^2)) − 5 + y)dy

should i take u substitution? for u=25 − (y^2), but how do i get rid of the other y?

Answer 1

\[\int\limits_{0}^{5}y \sqrt{25-y^2}-5+y)dy\] ?

Answer 2

Is that right?

Answer 3

If so I would split the integral into 3 parts
And use the substitution you have

Answer 4

for the first integral

Answer 5

The second two integrals will be very easy

Answer 6

As no substitution or tricks will be needed

Answer 7

After integrating
Don't forget about your limits of course :)

Answer 8

thank you!!

Answer 9

i just looked into it and realized the whole equations is in a parenthesis with y common, what do i do with that?