( 12 points ) Evaluate each of the definite integrals listed below 1 0 post ( 3 x ) dx " sin ( 2x ) sinx dx B * + 0 08 ( 2 x ) dx ( 6 points Apply the fundamental theorem of calculus to find the following derivative D I tan ( 30 ) at (8 points ) 8 A circular swimming pool has a diameter of 24 ft . , the sides are 5 ft . high , and the depth o the water is How much work is required to pump all of the water out over the side ? ( Use the fact hat water weighs 62 .5 1b / It ? ) ( 8 points ) 9 a . Sketch the region bounded by the curve D = 6 4x D = 8x a Find the area of the region sketched in part a ( 8 points ) A motorcycle starting from rest , speeds up with a constant acceleration of 2.6 m / s After it has traveled 120 m , it slows down with a constant acceleration of 1.5 m / s until it attains a ocity of 1 cle at that velocity of 12 m /s . What is the distance traveled by the motorcycle at that point ? Hint . Do not use decimals leave square roots indicated ( 6 points ) 1 1 2 . The temperature of a lo m long metal bar is 15 Cat one end and 30 ' Cat the other end Assuming that the temperature increases linearly from the cooler end to the hotter end , what is the average temperature of the bar ? Explain Why there must be a point on the bar where the temperature is the same as the average , and find