Hi all!
I'm trying to find the anti derivative of a(t)=cos(t)+sin(t)

so far I have sin(t)+c-cos(t) as the antiderivitive but Im confused because the antiderivitive of cos(t) is sin(t)+c and the antiderivitive of sin(t) is -cos(t)+c
so should the antiderivitive of a(t) be sin(t)+c-cos(t)+D??
just confused about the c/d thing.

Thanks!

The antiderivative of would be



No need for another constant.



Now, when we take the derivative of sin(t)-cos(t)+C we get back where we started. To cos(t)+sin(t).

Because the derivative of a constant, C, is 0.

Quote:

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Originally Posted by Gernald

Hi all!
I'm trying to find the anti derivitive of a(t)=cos(t)+sin(t)

so far I have sin(t)+c-cos(t) as the antiderivitive but Im confused because the antiderivitive of cos(t) is sin(t)+c and the antiderivitive of sin(t) is -cos(t)+c
so should the antiderivitive of a(t) be sin(t)+c-cos(t)+D ???
just confused about the c/d thing.

Thanks!

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It is impossible to identify the constant of integration. The solution which you seek lacks a closed form .

Quote:

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Originally Posted by ngasnier

It is impossible to identify the constant of integration. The solution which you seek lacks a closed form .

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Huh??
I'm just going to go with +c and be done with it.

Thanks anyway.