Para resolver a integral \( \int_{0}^{\pi} \cos^2(x) \, dx \), você pode usar a identidade: \[ \cos^2(x) = \frac{1 + \cos(2x)}{2} \] Substituindo na integral, temos: \[ \int_{0}^{\pi} \cos^2(x) \, dx = \int_{0}^{\pi} \frac{1 + \cos(2x)}{2} \, dx \] Agora, podemos separar a integral: \[ = \frac{1}{2} \int_{0}^{\pi} 1 \, dx + \frac{1}{2} \int_{0}^{\pi} \cos(2x) \, dx \] Calculando a primeira parte: \[ \frac{1}{2} \int_{0}^{\pi} 1 \, dx = \frac{1}{2} [x]_{0}^{\pi} = \frac{1}{2} (\pi - 0) = \frac{\pi}{2} \] Agora, a segunda parte: \[ \frac{1}{2} \int_{0}^{\pi} \cos(2x) \, dx = \frac{1}{2} \left[ \frac{\sin(2x)}{2} \right]_{0}^{\pi} = \frac{1}{2} \left( \frac{\sin(2\pi)}{2} - \frac{\sin(0)}{2} \right) = 0 \] Portanto, somando as duas partes: \[ \int_{0}^{\pi} \cos^2(x) \, dx = \frac{\pi}{2} + 0 = \frac{\pi}{2} \] Assim, a resposta final é: \[ \int_{0}^{\pi} \cos^2(x) \, dx = \frac{\pi}{2} \]