MATH 2B Chapter Notes - Chapter 5.4: Antiderivative

• School: UC-Irvine
• Department: Mathematics
• Course: MATH 2B
• Professor: George Donaldson

Document Summary

The fundamental theorem of calculus tells us that an anti-derivative of a continuous function f de- a f (t) dt. Ned on an interval cointaining a may be written f(x) = r x anti-derivatives and integrals we introduce a new notation for anti-derivatives: F(x) = z f (x) dx means the same thing as. If f is a function which has an anti-derivative, then the inde nite integral of f is denoted. This expression represents either: all anti-derivatives of f , a particular anti-derivative of f (rarely). function or a family of functions: indeed. Be careful: the de nite integral r b f (x) dx = (cid:20)z f (x) dx(cid:21)b. Z b a a a f (x) dx is a number, while the inde nite integral r f (x) dx is a. We can rewrite the table of anti-derivatives from section 4. 9 as inde nite integrals: 1 n + 1 xn+1, k constant n 6= 1.