Indica o valor de ( ) 4 2 4 2cos 1t dt π π − −∫. (A) -1 (B) 0 (C) 1 (D) 2

Para resolver a integral \(\int_{-\pi/4}^{\pi/4} \cos(2t) \, dt\), vamos calcular passo a passo. 1. A integral de \(\cos(2t)\) é \(\frac{1}{2} \sin(2t)\). 2. Agora, aplicamos os limites de integração: \[ \int_{-\pi/4}^{\pi/4} \cos(2t) \, dt = \left[ \frac{1}{2} \sin(2t) \right]_{-\pi/4}^{\pi/4} \] 3. Calculando os limites: \[ = \frac{1}{2} \sin\left(2 \cdot \frac{\pi}{4}\right) - \frac{1}{2} \sin\left(2 \cdot -\frac{\pi}{4}\right) \] \[ = \frac{1}{2} \sin\left(\frac{\pi}{2}\right) - \frac{1}{2} \sin\left(-\frac{\pi}{2}\right) \] \[ = \frac{1}{2} \cdot 1 - \frac{1}{2} \cdot (-1) \] \[ = \frac{1}{2} + \frac{1}{2} = 1 \] Portanto, o valor da integral é \(1\). A alternativa correta é: (C) 1.