Interpretation: We slice the area under a curve into infinitely thin rectangles, sum them up, and get the exact total.
Meaning: If you integrate a function and then differentiate the result, you get back the original function. calculus.mathlife
| 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: Interpretation: We slice the area under a curve
