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f"(x)>0, show that int(f(x)cosx dx) >0

Source: ISI(BS) 2009 #2

May 5, 2012

functioncalculusderivativeintegrationtrigonometryanalytic geometrygraphing lines

Problem Statement

Let

f(x)

be a continuous function, whose first and second derivatives are continuous on

[0,2\pi]

and

f''(x) \geq 0

for all

x

[0,2\pi]

. Show that

\int_{0}^{2\pi} f(x)\cos x dx \geq 0