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[ \fracddx \int_a^x f(t) , dt = f(x) ]
Interpretation: We slice the area under a curve into infinitely thin rectangles, sum them up, and get the exact total. calculus.mathlife
[ f'(x) = \lim_h \to 0 \fracf(x+h) - f(x)h ] [ \fracddx \int_a^x f(t) , dt = f(x)
Meaning: If you integrate a function and then differentiate the result, you get back the original function. [ \fracddx \int_a^x f(t)
Interpretation: We take two points on a curve, bring them infinitely close together, and measure the slope of the resulting tangent line.
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