A trough is 5 meters long and 1 meter high. The vertical cross-section of the trough parallel to an end is shaped like the graph of y = x² from x = −1 to x = 1. The trough is full of water. Find the amount of work (in joules) required to empty the trough by pumping the water over the top. (The acceleration due to gravity is 9.8 ms² and the density of water is 1000 kg m³.)