MATH 140 Lecture 31: Indefinite Integrals
19 Nov 2015
School
Department
Course
Professor
Document Summary
If f is any antiderivative of f on [a, b], then b a f ( x) dx=f (b) f (a: the big deal in evaluating b a f ( x) dx is finding an antiderivative of f, note: o. G( x)= x a f (t) dt g" ( x)=f ( x) ,a x b. That is, the derivative of the integral of f is f. x a f "(t ) dt=f ( x) f (a) Then f (x)dx represents the collection of all antiderivatives of f on [a, b]: f ( x) dx=f ( x)+c , where f is any antiderivative of f and c is a constant, important note: in webassign, when typing in the answers to integral problems, the c that represents the constant must be capitalized, note: suppose that g( x)=f ( x)=f "( x) for all x; then there is a constant c such that. Then g( b) g (a)=(f (b)+c ) (f (a)+c )
