Antiderivatives Part V

[Hckyplayer8]

The solution to the find the antiderivative problem f(x)(dx) was sinx - x cos x +C
What was f(x)?

If I'm tracking, this is basically asking f''(x) but in reverse. The question gives us the derivative of a function, which is the antiderivative of f''(x). Thus I am now challenged to find the original function.

Is that correct?

 

[Deleted member 4993]

The solution to the find the antiderivative problem f(x)(dx) was sinx - x cos x +C
What was f(x)?

If I'm tracking, this is basically asking f''(x) but in reverse. The question gives us the derivative of a function, which is the antiderivative of f''(x). Thus I am now challenged to find the original function.

Is that correct?

Are you saying:

If \(\displaystyle \int f(x) dx \ = \ sin(x) - x * cos(x) + C \):

What is f(x)?

Please post the EXACT problem (verbatim) as it was presented to you.

 

[Hckyplayer8]

Are you saying:

If \(\displaystyle \int f(x) dx \ = \ sin(x) - x * cos(x) + C \):

What is f(x)?

Please post the EXACT problem (verbatim) as it was presented to you.

That looks correct.

Here is a straight copy and paste.

(5): The solution to the find the antiderivative problem \(\displaystyle \int \) f(x) dx turned out to be sin x − x cos x + C. What is f(x)?

 

[Deleted member 4993]

That looks correct.

Here is a straight copy and paste.

(5): The solution to the find the antiderivative problem \(\displaystyle \int \) f(x) dx turned out to be sin x − x cos x + C. What is f(x)?

\(\displaystyle \frac{d}{dx}\left[\int f(x) dx \right] = f(x) \)

 

[Steven G]

The solution to the find the antiderivative problem f(x)(dx) was sinx - x cos x +C
What was f(x)?

If I'm tracking, this is basically asking f''(x) but in reverse. The question gives us the derivative of a function, which is the antiderivative of f''(x). Thus I am now challenged to find the original function.

Is that correct?

Please type f'(x) and NOT f"(x) for the derivative of f(x). Please?

 

[Dr.Peterson]

That looks correct.

Here is a straight copy and paste.

(5): The solution to the find the antiderivative problem \(\displaystyle \int \) f(x) dx turned out to be sin x − x cos x + C. What is f(x)?

\(\displaystyle \frac{d}{dx}\left[\int f(x) dx \right] = f(x) \)

In words, if an antiderivative of f is sin x - x cos x, that means f is the derivative of sin x - x cos x. What is that?

To put it another way, if you integrated a function and got sin x - x cos x + C, how would you check your result? You'd differentiate to see if you got your original function back.

 

[HallsofIvy]

An "anti-derivative" is the opposite of a derivative. To go from the "anti-derivative" to the original function, differentiate!