Two way system?

Calculus Level 1

f ( x ) d x = f ( x ) \int f'(x) \; \mathrm{d}x = f(x) Is the conclusion above always true?

Yes, it is always true No, it is not always true

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2 solutions

Ved Pradhan
Jul 1, 2020

Because of the constant C C , there are an infinite amount of functions that will come out of the left hand side of the equation, so you can't guarantee what comes out will be your original function.

Zakir Husain
Jul 2, 2020

f ( x ) d x = d f ( x ) d x d x = d f ( x ) = f ( x ) + C \int f'(x)dx=\int \frac{df(x)}{\cancel{dx}}\cancel{dx}=\int df(x)=f(x)+C C C is any constant

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