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- A TROUGH IS 4 METERS LONG, 2.5 METERS WIDE, AND 5 METERS DEEP. THE VERTICAL CROSS SECTION OF THE TROUGH PARALLEL TO THE END IS SHAPED LIKE AN ISOSCELES TRIANGLE WITH A HEIGHT OF 5 METERS AND A BASE, WHICH IS ON TOP OF 2.5 METERS. SO THE TROUGH IS PICTURED HERE. THE TROUGH IS FULL OF WATER THAT HAS A DENSITY OF 1,000 KILOGRAMS PER METERS CUBED. WE WANT TO FIND THE AMOUNT OF WORK IN JOULES REQUIRED TO EMPTY THE TROUGH BY PUMPING THE WATER OVER THE TOP. WEamp;#39;LL ALSO USE THE ACCELERATION DUE TO GRAVITY GIVEN HERE. BEFORE WE SET THIS UP THOUGH, IF AN OBJECT IS MOVING ALONG A STRAIGHT LINE BY CONTINUOUSLY VARYING FORCE F OF X THEN THE WORK DONE BY THE FORCE AS THE OBJECT IS MOVED FROM X = amp;quot;Aamp;quot; TO X = B IS GIVEN BY THIS DIFF INTEGRAL. TO UNDERSTAND WHY THIS WORKS, IF YOU CONSIDER 1 INCREMENT OF WORK WHICH WOULD BE THE AMOUNT OF WORK REQUIRED TO PUMP ONE LAYER OF WATER OUT OF THE TANK IT WOULD BE EQUAL TO THE FORCE x THE DISTANCE INCREMENT. AND AS WE FOUND THE SUM OF M