Question

Find the antiderivative.

f(x) = x^2

Answer 1

use power rule

Answer 2

\[\large \int x^n dx = \frac{x^{n+1}}{n+1}\]
do you get that? or do you need more help?

Answer 3

more help please

Answer 4

If you compare your equation to his, what is n?

Answer 5

hint: n is the exponent of x in my example

Answer 6

hmm sorry im still confused

Answer 7

what is the exponent in this problem?

Answer 8

2

Answer 9

2x

Answer 10

2 is the exponent right so what did i do with the exponent in
\[x^n dx = \frac{x^{n+1}}{n+1}\]

Answer 11

@student92 anti-derivative, not the derivative. Also, please don't just give out the answer without anything else as that's against the code of conduct: http://openstudy.com/code-of-conduct

Answer 12

put it where n is

Answer 13

okay here's a more visual hint
\[\large \int x^3 dx = \frac{x^{3+1}}{3+1} = \frac{x^4}{4}\]

Answer 14

do you see it?

Answer 15

yes

Answer 16

but thats not the antiderivative right?

Answer 17

It's the antiderivative to the example he posted. To prove it you can take the derivative of (X^4}/4 and see if you get X^3 as the result.

Answer 18

oh got it

Answer 19

so do you now know what is \[\int x^2 dx?\]

Answer 20

no...

Answer 21

okay another hint
\[\huge \int x^4 dx \implies \frac{x^{4+1}}{4+1} \implies \frac{x^5}{5}\]

Answer 22

so thats the antiderivative

Answer 23

?

Answer 24

It's the anti-derivative of his example. Do you know what an anti-derivative is?

Answer 25

yes, inverse of the derivative

Answer 26

it just follows the rule \[\int x^n dx = \frac{x^{n+1}}{n+1}\]
n is the exponent

Answer 27

here's another one...
\[\large \int xdx \implies \int x^1 dx \implies \frac{x^{1+1}}{1+1} \implies \frac{x^2}{2}\]

Answer 28

do you see what is \[\int x^2 dx\] yet?

Answer 29

yes i believe so

Answer 30

int(x^3) = (1/4)x^4
int(x^5) = (1/6)x^6
int(x^32) = (1/33)x^33
int(x^2) = ?

Answer 31

(1/3)x^3?

Answer 32

:)

Answer 33

awesome thanks!!!!

Answer 34

fo sure

Answer 35

Now try this one. What function has antiderivative = derivative of the function.
If you can work that out. You'll understand how awesome e is.

Answer 36

now take the derivative of that just for fun.

Answer 37

prooving that said function is the ONLY antiderivative = derivative is sort of hard at this point im thinking