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| 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:

To compute a definite integral (total accumulation), evaluate the antiderivative at the endpoints and subtract. calculus.mathlife

Interpretation: We take two points on a curve, bring them infinitely close together, and measure the slope of the resulting tangent line. | Integral ( \int f(x) , dx )