MathDB
Today's calculation of Integral 232

Source: Tokyo University entrance exam/Science 1995

October 9, 2007
calculusintegrationtrigonometryinequalitiescalculus computations

Problem Statement

For f(x)\equal{}1\minus{}\sin x, let g(x)\equal{}\int_0^x (x\minus{}t)f(t)\ dt. Show that g(x\plus{}y)\plus{}g(x\minus{}y)\geq 2g(x) for any real numbers x, y. x,\ y.