Question

I have to find the most general antiderivative f(X)= pi^6

Answer 1

As you know, \(\pi^6\) is a constant. Therefore, the variable x in the anti-derivative has teh power of 1. Have you figure it out from here?

Answer 2

yep

Answer 3

Can you share the answer?

Answer 4

My answer is \(\pi^6x+C\)

Answer 5

i had pi^6x

Answer 6

so most general antiderivative is just another way to say "find the derivative"?

Answer 7

Well done.

Answer 8

i meant the antiderivative

Answer 9

Yeah, almost.

Answer 10

For example, your answer for this problem is \(\pi^6x\). It is correct. However, the most general antiderivative will be \(\pi^6x+c\).
Because \(\int(\pi^6)dx =\pi^6x\). But \(\int(\pi^6)dx =\pi^6x+1\) or \(\pi^6x+2\) and so on, right?

Answer 11

So they use \(c\) to write the most general antiderivative, always, after find the antiderivative

Answer 12

i see

Answer 13

There are soee more examples here.
http://www-math.mit.edu/~djk/calculus_beginners/chapter16/section01.html

Answer 14

thanks

Answer 15

You are welcome