Two integral mean value theorems of flett type

Continuous function, integrals, graphs, Mean-Value TheoremIf f is continuous on the closed interval [a,b] and f(a)=f(b), then there exist c and d in (a,b) such that (c - a)f(c) = ∫f(x)dx to a from c and (b - d)f(d)=∫f(x)dx to d from b. The theorem is illustrated by the equivalence of the blue and striped areasComponente Curricular::Educação Superior::Ciências Exatas e da Terra::Matemátic