Question

find the integral y√(2+10y−25y^2) dy

Answer 1

wouldnt (y^2-2/5y+1/25) be to the 3/2?

Answer 2

Oh there's a y in front of the integral?
Did you edit the question?
Or did I completely miss that..?
Oh boy..

Answer 3

I went the same route but i got this answer C-(1/25)(-25y^2+10y+2)^(3/2)+(1/50)(5y-1)sqrt(-25y^2+10y+2)(3/50)sin^-1((5y-1)/sqrt3))

Answer 4

and haha I didnt edit it, the y was originally there

Answer 5

oh wow im so confused now

Answer 6

WHAT is the question?!?

Answer 7

This is the question:\[\large\rm \int\limits y\sqrt{2+10y-y^2}~dy\]

Answer 8

yes

Answer 9

is that a simple question or ami sleepy?

Answer 10

just jooooking that's not an easy Q "D"

Answer 11

hmm it's -25y^2 -.p

Answer 12

Can't apply U sub so integration by parts I think.

Answer 13

It is of the format - \[\int(Px+Q) \sqrt{ax^2+bx+c}\]

Answer 14

Let u = y and dv = sqr(stuff)

Answer 15

In such cases we just put Px+Q=l(derivative of stuff under sqrt) +m where l and m are any two numbers which u can find by comparing the RHS and LHS

next you write the integral like this-
\(\int l(derivative ~of ~stuff~under~sqrt)+m\sqrt{ax^2+bx+c}\)


And then you open the parentheses and split the integral

Answer 16

Aww i forgot to put l(derivative of stuff) +m in parentheses in that integral

Answer 17

An integration using the Mathematica program is attached.