Today's calculation of Integral 553
Source: 2010 Doshisya University entrance exam/Life Science
February 7, 2010
calculusintegrationfunctiontrigonometrycalculus computations
Problem Statement
Find the continuous function such that f(x)\equal{}\frac{e^{2x}}{2(e\minus{}1)}\int_0^1 e^{\minus{}y}f(y)dy\plus{}\int_0^{\frac 12} f(y)dy\plus{}\int_0^{\frac 12}\sin ^ 2(\pi y)dy.