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?

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?

myininaya · Answer

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

myininaya · Answer

Is that right?

myininaya · Answer

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

myininaya · Answer

for the first integral

myininaya · Answer

The second two integrals will be very easy

myininaya · Answer

As no substitution or tricks will be needed

myininaya · Answer

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

anonymous · Answer

thank you!!

anonymous · Answer

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