Let f(x)=∣2cos⁡x1012cos⁡x1012cos⁡x∣f(x) = \begin{vmatrix} 2 \cos x & 1 & 0 \\ 1 & 2 \cos x & 1 \\ 0 & 1 & 2 \cos x \end{vmatrix}…

Mathematics

Problem

Let f(x)=∣2cos⁡x1012cos⁡x1012cos⁡x∣f(x) = \begin{vmatrix} 2 \cos x & 1 & 0 \\ 1 & 2 \cos x & 1 \\ 0 & 1 & 2 \cos x \end{vmatrix} , then a. f(π3)=−1f\left(\frac{\pi}{3}\right) = -1 b. f(π3)=3f\left(\frac{\pi}{3}\right) = \sqrt{3} c. ∫0πf(x)dx=0\int_{0}^{\pi} f(x) dx = 0 d. ∫−ππf(x)dx=0\int_{-\pi}^{\pi} f(x) dx = 0

Browse the problem library