Today's calculation of Integral 575
Source: 2010 Kumamoto University entrance exam/Medical
March 4, 2010
calculusintegrationfunctionlogarithmstrigonometrycalculus computations
Problem Statement
For a function f(x)\equal{}\int_x^{\frac{\pi}{4}\minus{}x} \log_4 (1\plus{}\tan t)dt\ \left(0\leq x\leq \frac{\pi}{8}\right), answer the following questions.
(1) Find .
(2) Find the th term of the sequence such that a_1\equal{}f(0),\ a_{n\plus{}1}\equal{}f(a_n)\ (n\equal{}1,\ 2,\ 3,\ \cdots).