Analysis - Fundamental Theorem of Integral Calculus

Описание к видео Analysis - Fundamental Theorem of Integral Calculus

Q1: Find a continuous function f and a constant a such that
(a) \int_a^x f(t) dt = (1 - cos(x^2))/2, for all real number x;
(b) \int_a^x f(t) dt = x^2 + 4x - 5, for all real number x.

Q2: Let f be a continuous function on [0, 1]. Suppose that
\int_0^x f(t) dt = \int_x^1 f(t) dt, for all x in (0, 1).
Find f(t).

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