# Thread: mean value theorem

1. ## mean value theorem

Can someone please show me or tell me why the Mean Value Theorem for integrals is a special case of the generalized Mean Value Theorem for integrals.

Mean Value Theorem for Integrals: If f is continuous on [a,b], then there exists a point cE[a,b] such that f(c)(b-a)= inetgral of f from a to b.

generalized Mean Value Theorem: If f is continuous on [a,b] and g is nonnegative Riemann integrable function on [a,b], then there exists a point cE[a,b] such that f(c) integral of g from a to b = integral of fg from a to b.

2. Originally Posted by summerset353
Can someone please show me or tell me why the Mean Value Theorem for integrals is a special case of the generalized Mean Value Theorem for integrals.

Mean Value Theorem for Integrals: If f is continuous on [a,b], then there exists a point cE[a,b] such that f(c)(b-a)= inetgral of f from a to b.

generalized Mean Value Theorem: If f is continuous on [a,b] and g is nonnegative Riemann integrable function on [a,b], then there exists a point cE[a,b] such that f(c) integral of g from a to b = integral of fg from a to b.
In the generalized Mean Value Theorem consider $g(x)=1$.