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