Today's calculation of Integral 265
Source: 1985 Waseda University entrance exam/Education
January 11, 2008
calculusintegrationtrigonometrycalculus computations
Problem Statement
Supposed that has and for any real numbers , \int_y^{x \plus{} y} f(t)\ dt \equal{} \int_0^x \{f(y)\cos t \plus{} f(t)\cos y\}\ dt holds.
(1) Express f(x \plus{} y) in terms of
(2) Find f'\left(x \plus{} \frac {\pi}{2}\right). Note that f\left(\frac {\pi}{2}\right) \equal{} 2.
(3) Find