Let f and h be two integrable functions in [a,b]. Let M=sup|f(x)| when x in [a,b].

Prove that:

| int{f(x)*h(x)}dx | <=M*int{| h(x) |}dx

(The both integrals are from a to b)

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- Apr 6th 2010, 04:27 AMAlso sprach ZarathustraIntegrals problem 1
Let f and h be two integrable functions in [a,b]. Let M=sup|f(x)| when x in [a,b].

Prove that:

| int{f(x)*h(x)}dx | <=M*int{| h(x) |}dx

(The both integrals are from a to b) - Apr 6th 2010, 05:33 AMgirdav
We have $\displaystyle \left|\int_a^bf\left(x\right)g\left(x\right)dx \right|\leq \int_a^b\left|f\left(x\right)g\left(x\right)\right | dx =\int_a^b\left|f\left(x\right)\right|\left|g\left( x\right)\right| dx \leq \int_a^bM\cdot \left|g\left(x\right)\right| dx $

- Apr 6th 2010, 07:53 AMAlso sprach Zarathustra
May you please do it by Reimann or Darboux sums?

- Apr 6th 2010, 08:04 AMDrexel28