Question

Evaluate the definite integral of the algebraic function.Use a graphing utility to verify your results.

Answer 1

how do i figure this out?

Answer 2

It's making simple things hard :D
\[\huge \int z^mdz=\frac{z^{m+1}}{m+1}\]

Answer 3

You add one to the exponent and then divide the entire thing by that new exponent :D
With that in mind
\[\huge \int\limits_3^6 \left(z^{\frac95}+z^{\frac59}\right)dz\]

Answer 4

Start with
\[\huge z^{\frac95}\]
remember...
ADD 1 to the exponent
DIVIDE the whole thing by that new exponent.

Answer 5

hmmm.... idk how i got 31.8? i evaluated the integral

Answer 6

Well, ^ that thing above... add 1 to its exponent, and divide the whole thing by that new exponent like this
\[\huge \frac{z^{\frac95+1}}{\frac95 +1}=\frac{5z^{\frac{14}{5}}}{14}\]

Answer 7

Now, do the same to
\[\huge z^{\frac 59}\]

Answer 8

i got 28.9667 to z5/9

Answer 9

@PeterPan

Answer 10

Don't do any evaluating yet, just get the antiderivative... by doing what I told you~ add 1 to the exponent, divide the whole thing by that new exponent.

Answer 11

27/5 would be the derivative of that wouldnt it?

Answer 12

No... that's a constant?

Answer 13

i dont know.. i cant figure this out

Answer 14

Do something similar to what I did.
Just add 1 to the exponent, then divide the whole thing by that new exponent
then simplify
\[\huge z^{\frac95}\]
\[\huge \frac{z^{\frac95+1}}{\frac95 +1}=\frac{5z^{\frac{14}{5}}}{14}\]

do it for
\[\huge z^{\frac59}\]

Answer 15

how did you get 14 for that ?

Answer 16

\[\huge \frac95 + 1\]