explain with solution. thank you

basic calculus

PART I. Evaluate the following integrals. Show all the necessary solutions. 2x3+5x24 1.} dxxz 2. I (6x2 ux 3. j (1 + 3t)t2dt 4.; W + 10de 5. I (c2 1)(4 + 3t)dt 6.1 sin(x) + 10cscz(x)dx 7.112 dy PART [1. Problem Solving. Choose the correct answer. Write your answer on the space provided before the number.(5pts.) 1. We need to enclose a rectangular field with a fence. We have 300 feet of fencing material and a building is on one side of the field and so won't need any fencing. Determine the dimensions of the field that will enclose the largest area. 2. An airplane is ying towards a radar station at constant height of 6 km above the ground. If the distance 5 between the airplane and the radar station is decreasing at a rate of 400 km per hour when 5 = 10km, what is the horizontal speed of the plane? 3. A ladder 8 m long leans against a model home. If the bottom of the ladder slides away from the building horizontally at a rate of 0.75 m/sec, how fast is the ladder sliding down the model home when the top of the ladder is 5m from the ground