Question

Can someone explain to me this integration, i know cosx differentiates to -sinx, but how is it that the anti derivative of sinx with respects to f is -cosx+c

Answer 1

for an antiderivative theres always an extra constant that could arise, hence the c

Answer 2

but i mean the - cosx part

Answer 3

how do we get a -cosx

Answer 4

because the derivative of -cosx
is-(-sinx)=sinx

Answer 5

i think you meant to say with repsect to x

Answer 6

i still dont get it

Answer 7

if i was just given like sinx and told to intergrate, what would be my process

Answer 8

if you want to formulaic way of integrating sin x, it wouldn't be very easy. It involves trigonometric proofs and identities

Answer 9

oh i get it, if i want to derive sinx, then what i have to do is realize that cosx defferintaites to -sinx, but since i want just sinx i have to have a negative sign .

Answer 10

We usually find antiderivatives through derivatives themselves.
For example if we have an equation F(x)=x^2, taking the derivative would be F'(x)=2x.
If we were to go from 2x to x^2, it would be taking the antiderivative

Answer 11

Precisely, that's one of the tough challenges of calculus, trying to understand trigonometric properties :/

Answer 12

Another good example is 1/x. If you were to integrate 1/x, your answer would end up with an undefined answer. However we know that the derivative of 1/x is ln x, therefore ln x is the antiderivative of 1/x. Hope this helps! :)