Calculus.mathlife Link -

Differentiation and integration are inverse operations.

| Integral ( \int f(x) , dx ) | Result (plus constant ( C )) | | :--- | :--- | | ( \int x^n , dx ) (n ≠ -1) | ( \fracx^n+1n+1 ) | | ( \int \frac1x , dx ) | ( \ln |x| ) | | ( \int e^x , dx ) | ( e^x ) | | ( \int \cos x , dx ) | ( \sin x ) | | ( \int \sin x , dx ) | ( -\cos x ) | This theorem connects the two pillars. It says: calculus.mathlife

[ \fracddx \int_a^x f(t) , dt = f(x) ]

[ f'(x) = \lim_h \to 0 \fracf(x+h) - f(x)h ] Differentiation and integration are inverse operations