Question

Anti-differentiation help?

Answer 1

http://prntscr.com/3b2pht

Answer 2

are you sure this is anti-derivative?

Answer 3

Yes sir~

Answer 4

\[\int\limits f'(x) dx=\frac{ 2x^{3+1} }{ 3+1 }+C\]
then we need to find C

Answer 5

Yup, but how would we find it given just the tangent line?

Answer 6

the tangent line gives you a clue where it lies

Answer 7

is this your first time doing this kind of problem?

Answer 8

First time doing it given a tangent equation.

Answer 9

do you know that the constant tells us the kind of family of equation we have?

Answer 10

well that we have a family of equations before us

Answer 11

y = -2x has a slope of -2

so find the value of x such that f'(x) = -2

Answer 12

use that x to find y.

the integrate f'(x) and use that (x,y) to find the constant

Answer 13

Alright, let me try it.