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Problem Compute ∫ 0 π / 4 θ 3 sin ( θ 2 ) d θ \displaystyle \int_{0}^{\pi/4} \theta^{3}\sin\!\left(\theta^{2}\right)\,d\theta ∫ 0 π /4 θ 3 sin ( θ 2 ) d θ 1 2 [ π 2 16 cos ( π 2 16 ) + sin ( π 2 16 ) ] \displaystyle \tfrac12\bigl[\tfrac{\pi^{2}}{16}\cos(\tfrac{\pi^{2}}{16})+\sin(\tfrac{\pi^{2}}{16})\bigr] 2 1 [ 16 π 2 cos ( 16 π 2 ) + sin ( 16 π 2 ) ] 1 2 [ − π 2 16 cos ( π 2 16 ) + sin ( π 2 16 ) ] \displaystyle \tfrac12\bigl[-\tfrac{\pi^{2}}{16}\cos(\tfrac{\pi^{2}}{16})+\sin(\tfrac{\pi^{2}}{16})\bigr] 2 1 [ − 16 π 2 cos ( 16 π 2 ) + sin ( 16 π 2 ) ] 1 2 [ − π 4 cos ( π 4 ) + sin ( π 4 ) ] \displaystyle \tfrac12\bigl[-\tfrac{\pi}{4}\cos(\tfrac{\pi}{4})+\sin(\tfrac{\pi}{4})\bigr] 2 1 [ − 4 π cos ( 4 π ) + sin ( 4 π ) ] − π 2 16 cos ( π 2 16 ) + sin ( π 2 16 ) \displaystyle -\tfrac{\pi^{2}}{16}\cos(\tfrac{\pi^{2}}{16})+\sin(\tfrac{\pi^{2}}{16}) − 16 π 2 cos ( 16 π 2 ) + sin ( 16 π 2 ) Browse the problem library