Problema 3. Sea $f:\left[ 0,\frac{\pi }{2} \right]\to \left[ 0,\infty \right)$ una función creciente. Probar que: (a) $\int_{0}^{\frac{\pi }{2}}{\left( f\left( x \right)-f\left( \frac{\pi }{4} \right) \right)}\left( \sin x-\cos x \right)dx\ge 0.$ (b) Existe $a\in \left[ \frac{\pi }{4},\frac{\pi }{2} \right]$ tal que $\int_{0}^{a}{f\left( x \right)\sin x\ dx=}\int_{0}^{a}{f\left( x \right)\cos x\ dx}.$