I need to proove the Minkowski's inequality for integrals.(adsbygoogle = window.adsbygoogle || []).push({});

I am taking a course in analysis.

[ int(f+g)^2 ] ^(1/2) =< [int(f^2)]^(1/2) + [int(g^2)]^(1/2)

now we are given that both f and g are Riemann integrable on the interval.

So by the properties of Riemann integrals, so is f^2,g^2 and fg.

We are also given a hint to expand the integral on the left and then use the Cauchy-Bunyakovsky-Schwarz inequality (now this i've already prooved in a previous exercice using the discriminant).

I was trying to expand the left side but i don't know what to do with the squared root, moreover i was trying to expand regardless the squared root and then at the end take a squared root but it still hasn't worked..

I need help =)

Thanks,

Joe

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# Minkowski's inequality!

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