Calculus.mathlife __full__ May 2026
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.
[ \int_a^b f(x) , dx = F(b) - F(a) ]
[ \fracddx \int_a^x f(t) , dt = f(x) ]
[ \int_a^b f(x) , dx = \lim_n \to \infty \sum_i=1^n f(x_i^*) \Delta x ]
| 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
Meaning: If you integrate a function and then differentiate the result, you get back the original function.
Interpretation: We slice the area under a curve into infinitely thin rectangles, sum them up, and get the exact total. Pick a single problem type (e
Where ( F ) is any antiderivative of ( f ).