MATH 2B Lecture Notes - Lecture 5: Antiderivative

• School: UC-Irvine
• Department: Mathematics
• Course: MATH 2B
• Professor: ERJAEE, G.

Document Summary

Math 2b - lecture 5 - indefinite integral and net change theorem. From fundamental theorem of calculus, we know that: Part i: g"(t) = (x) dx f(t) f t dt d a b a. Which indicates that the derivative and the integral are opposite operations. We then introduce a new notation for antiderivatives, the indefinite integral f (x)dx. + g (x))dx g (x)dx f (x)dx xk + c s inx dx s. 2 ec x dx s ecx tanx dx dx dx k ex xn dx (f(x) x +12 bx. 1 dx dx osx dx c c 2 sc x dx scx cotx dx c xn+1 + c n+1 (n = ) + c bx lnb + c sinx + c. + c dx s 1 + c in x. 1 cosx dx anx secx dx t secx. It is important to differentiate between the indefinite integral and definite integral. The most general antiderivative b a f (x)dx.