∫ π 4 5 π 4 cos t sin t + sin t cos t d t =

Step-by-step solution

I = ∫ π 4 5 π 4 cos t sin t + sin t cos t d t = ∫ π 4 π 2 cos t sin t d t - ∫ π 2 5 π 4 cos t sin t d t + ∫ π 4 π sin t cos t d t - ∫ π 5 π 4 sin t cos t d t = t 2 2 1 2 1 - t 2 2 1 - 1 2 + t 2 2 1 2 0 - t 2 2 0 - 1 2 (let sin t = t ) = 1 2 - 1 4 - 1 4 + 1 2 + 0 - 1 4 - 1 4 + 0 = 0 = 5 π 2 4 - 13 π 2 8