Let be a continuous functions for all

MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Let f(x)f(x) be a continuous functions for all xx , such that (f(x))2=∫0xf(t)⋅2sec⁡2t4+tan⁡tdt(f(x))^2 = \int_{0}^{x} f(t) \cdot \frac{2 \sec^2 t}{4 + \tan t} dt and f(0)=0f(0) = 0 , then (1) f(π4)=log⁡54f\left(\frac{\pi}{4}\right) = \log \frac{5}{4} (2) f(π4)=34f\left(\frac{\pi}{4}\right) = \frac{3}{4} (3) f(π2)=2f\left(\frac{\pi}{2}\right) = 2 (4) None of these

Related theory

Browse the problem library