Question

Evaluate the integral.

Answer 1

\[\int\limits_{5}^{4}(2+2y)^{2}dy\]

Answer 2

use u substitution
let u= 2+2y
then du = 2dy
so dy = du/2

so your integral should look like this

\[\int\limits_{5}^{4} 1/2(u)^2 du \]
you can integrate that right?

Answer 3

just plug in the values right

Answer 4

just integrate 1/2u^2 first and then replace the value back in

Answer 5

i got 4.5

Answer 6

I'm not sure why your lower limit of integration is larger than your upper limit.
In any case, you should end up with a negative answer.
It's the integral evaluated at 4, then you subtract from that, the integral evaluated at 5.

Answer 7

sorry i think you made a little mistake i show you
from here
\[\int\limits_{5}^{4} 1/2(u)^2 du\]

so integrate 1/2u^2 first and get
\[1/6(u)^3\]

once you have that replace the original value back in since u= 2+2y
now you get this
\[1/6(2+2y)^3 \]
and you evaluate that from 5 to 4
so you plug it like this

1/6(2+2(4))^3 - 1/6(2+2(5))^3
simplify and get -11

Answer 8

thanks

Answer 9

np glad to help