Question

Calculus: U-Substitution:
How would one go about integrating this using u-sub?

Answer 1

ok lets do this
let
\[\Large u=9t^4+1\]
then
\[\Large du=36t^3dt\]
or
\[\Large \frac{1}{36}du=t^3dt\]
so integral becomes
\[\Large \int\limits_{0}^{2}\frac{1}{36}\sqrt{u}du\]
can you do this now ?

Answer 2

and yes i made an error can you identify what it is !!! most of the students commits this mistake in paper !!!!!!!!

Answer 3

would it be the 1/36 goes on the other side of the integral?

Answer 4

oops ! yes it will but there is big big mistake look at the integral again !!!

Answer 5

U don't see any other error here ...

Answer 6

ok do not be upset !!! it is i did substitution u=9t^4+1
i did not change the limits !!!
so remember whenever in definite integral you use some substitution always change limits.
so
u=9t^4+1
when t=0
u=9(0)^4+1=1
when t=2
u=9(2)^4+1=145
so correct integral is now

\[\Large \frac{1}{36}\int\limits_{1}^{145}u^{\frac{1}{2}}du\]

Answer 7

hope you can do this now
can you?

Answer 8

Yes, I believe so! Thanks!

Answer 9

you 're welcome :)