Calculus.mathlife ((exclusive)) (TOP)

Meaning: If you integrate a function and then differentiate the result, you get back the original function.

Pick a single problem type (e.g., finding velocity from position) and solve 5–10 practice problems. Then move to the next. Mastery comes from doing, not just reading. calculus.mathlife

To compute a definite integral (total accumulation), evaluate the antiderivative at the endpoints and subtract. Meaning: If you integrate a function and then

Interpretation: We slice the area under a curve into infinitely thin rectangles, sum them up, and get the exact total. Mastery comes from doing, not just reading

[ f'(x) = \lim_h \to 0 \fracf(x+h) - f(x)h ]

| Function ( f(x) ) | Derivative ( f'(x) ) | | :--- | :--- | | Constant ( c ) | 0 | | ( x^n ) | ( n x^n-1 ) | | ( e^x ) | ( e^x ) | | ( \ln x ) | ( 1/x ) | | ( \sin x ) | ( \cos x ) | | ( \cos x ) | ( -\sin x ) | Core Question: What total amount builds up from a continuously changing rate?

[ \int_a^b f(x) , dx = \lim_n \to \infty \sum_i=1^n f(x_i^*) \Delta x ]