MathDB

644

Part of 2010 Today's Calculation Of Integral

Problems(1)

Today's calculation of Integral 644

Source:

9/4/2010
For a constant pp such that ∫1pexdx=1\int_1^p e^xdx=1, prove that (∫1pexcos⁡x dx)2+(∫1pexsin⁡x dx)2>12.\left(\int_1^p e^x\cos x\ dx\right)^2+\left(\int_1^p e^x\sin x\ dx\right)^2>\frac 12.
Own
calculusintegrationtrigonometryinequalitieslogarithmscalculus computations