Question 1 10 pts am: When a particle is located a distance 3 meters from the origin, a force of COS (?) newtons acts on it. How much work is done in moving the particle from a: = 1 to a: = 2? Interpret your answer by considering the work done from :12 : 1 to :12 : 1.5 and from :1: : 1.5 to :1: : 2. if your answer is not a whole number, enter it as a decimal rounded to three places. Do not include units. Question 2 10 pts The table shows values of a force function f(:1?), where :1: is measured in meters and at) in newtons. Use the Midpoint Rule with four subintervals to estimate the work done by the force in moving an object from a: = 4 to a: : 20. Enter a number only for your answer (no units). Force Function Values 6 8 101214161820 5 5.8 7.0 8.8 9.6 8.2 6.7 5.2 4.1 a/ Question 3 10 pts If (H of work is needed to stretch a spring from 10 cm to 12 cm and another 10 J is needed to stretch it from 12 cm to 14 cm, what is the natural length of the spring (in centimeters)? Enter a number oniy for your answer {no units). Question 4 10 pts Find the average value of the function f(a) = (203 + 3) 2 on the interval [-1, 1]. If your answer is not a whole number, enter it as a decimal rounded to three places.Question 5 10 pts In u Find the average value of the function h(u) = on the interval [1, 5]. If your answer is not a whole number, enter it as a decimal rounded to three places.Question 6 10 pts Find the possible values of b such that the average value of f (a) = 2 + 6x - 3x:2 on the interval [0, b] is equal to 3. O b = 3+15 2 O b = 3+ V29 2 Ob = 12 Ob = 13