Integral with U sub!

- anonymous

Integral with U sub!

- katieb

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- anonymous

integral y^2 (1+y)^2 dy

- anonymous

My work:
u = 1+y
du/dy = 1
du=dy?

- anonymous

then integral (1+y)^2 dy
integral u^2 du

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## More answers

- anonymous

(1_y)^3/3 +c

- anonymous

*(1+y)^3

- anonymous

do i keep the y^2?

- anonymous

ohh ok.. but what about u sub?

- anonymous

will u now be y^2+y^4?

- anonymous

well my teacher made this worksheet specifically for u sub :(

- anonymous

but i got 1 for u sub anyways. so i just keep y^2 ?

- anonymous

no

- anonymous

it's y^2 (1+y)^2

- anonymous

the square is outside the parenthesis

- stamp

I see my mistake. Let me reevaluate the problem and I will come at you with a response.

- zepdrix

Yah you wouldn't use a `U sub` for this one I'm afraid swin. You would just expand out the brackets and integrate each term individually.

- stamp

\[y^2(1+y)^2dy=y^2(y^2+2y+1)dy=(y^4+2y^3+y^2)dy\]

- anonymous

i didn;t know i had to lol oops

- anonymous

is there an indication to do so?

- stamp

No, you are simplifying your y terms and happen to end up with \[ (y^4+2y^3+y^2)dy \]Integrate each term dy

- anonymous

oh ok. that makes sense. usually i don't have to expand a problem or distribute so i didn't know if using u sub for 1+y is correct

- stamp

Had you done some usub, you would had \[(y^2u)du\] and would not really have gotten anywhere as far as the integral goes. Be sure to have + C to your integral term since the integral is undefined.

- zepdrix

To apply a `u sub`, you want to look for a suitable `u` and `u'` somewhere in your problem.
\(2y(1+y^2)\)
See how if \(u=1+y^2\) then \(u'=2y\) ?
In the problem you were given, letting your inner function be `u` did NOT result in the outer function being u'. So that is usually your indicator.

- anonymous

OHH ok! I'll make sure to tell my teacher to clarify this to the class. I did not know that! hahaha

- anonymous

oh but in the case you're presenting it's (1+y^2)
not (1+y)^2

- anonymous

u sub can be used when the exponent is outside right?

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