i need help with calculus study questions

QUESTION 1 Which statement is true for a positive valued function f(x)? The average value of the function between (a, b), is the area under the curve of f '(x) between (a, b) The average value of the function between (a, b), is the area under the curve of f(x) between (a, b) divided by (b-a) The average value of the function between (a, b), is the average of f(b) and f(a). The average value of the function between (a, b), is the area under the curve of f(x) between (a, b). QUESTION 2 If an object's movement, distance over time, is modeled as d(t), then which of the following can be used to describe the average distance the object has moved The average value of d '(t). ( The average value of d(t). The Mean Value Theorem applied to d(t) The Mean Value Theorem applied to d '(t) QUESTION 3 What is the average value of f(x), between x = 1 and x = 4 for f x) = 3X_I ? O 0.568 0.675 0.667 O 1.337 QUESTION 4 What is the average value of f(x), between x = 0 and x = 2TT , where f(x) = sin(x)? O 2TT 0 1 OO\f