Assignment #5: The Fundamental Theorem of Calculus Doew In Exercises 1-6, find the average value of the function over the given interval and all values of c in the interval for which the function equals its average value. 1. f (x) = 4 -x2, [-2,2] 2. f(x) = 4x3 - 3x2, [0,1] 3. f(x) = 4(x2+1) x2 , [1,3] 4. f(x) = sin x , [0, 7] 5 . f (x ) = cosx, (0, 7 ] 6. f(x) = Vx, [4,9]In Exercises 7-10, use the Second Fundamental Theorem of Calculus to find F (x). 7. S ( +2 - 2t ) dt 8. S Vt+ + 1 dt 12 1 72+1 10. fx sect tant dt In Exercises 11-14, find each derivate. d [vx t d sin * 1 - t2 dt 11. 12. - So 13. a *+2 ( 4t + 1) at ax J_ sint dt15. The graph of y = So f(t)dt, where f is a piecewise constant function, is shown below. 0 5 X a.) Over which intervals is f positive? b.) Over which intervals is f negative? c.) Over which intervals, if any, is it equal to zero? d.) What are the maximum and minimum values of f