/sci/ - Science & Math

so I know the FDC theorem states that I can find one of the anti derivatives of the function or a specific one if Im given a bounded interval.

Its easy to find the antiderv if Im given the function, but my text book only states it as f(x)

So I have this: integral f(x)dx = 10 between 0 to 4. It then asks me to evaluate the integral of f(2x)dx between 0 to 2. (the answer is 5). (pic related)

Now I would have gotten the result long ago if I was given the goddamn function and not just f(x). I imagine its related to the first theorem. (which Ive done many exercises but I was given a function and I just had to plug in x or do some variable substitution.

Basically, is it possible to find the anti derivative, without the function, if only given the area and/or the bounded interval?

Btw is my description of the FTC-Theorem right or am I wrong? Thanks.

so I know the FDC theorem states that I can find one of the anti derivatives of the function or a specific one if Im given a bounded interval.

Its easy to find the antiderv if Im given the function, but my text book only states it as f(x)

So I have this: integral f(x)dx = 10 between 0 to 4. It then asks me to evaluate the integral of f(2x)dx between 0 to 2. (the answer is 5). (pic related)

Now I would have gotten the result long ago if I was given the goddamn function and not just f(x). I imagine its related to the first theorem. (which Ive done many exercises but I was given a function and I just had to plug in x or do some variable substitution.

Btw is my description of the FTC-Theorem right or am I wrong? Thanks.