Question

Evaluate \[ \int_{-1}^1 18 t^5 ( 1+ t^6) dt \]

There are two for doing this one short way that does not
need any computation and one that a bit longer.
Either way will be fine.

Answer 1

you can multiply out easily to get \(18t^5+18t^{11}\)
you can also use a u-sub but that is unnecessary

Answer 2

think there is a typo here
is it
\[\int_{-1}^1 18t^5(1+t^6)dt\]?

Answer 3

if so compute nothing
you have an odd function so integral will be zero

Answer 4

From -1 to 1

Answer 5

then it is zero for sure

Answer 6

if \(f\) is odd then \(\int_{-a}^a f(x)dx=0\)