please help Find the average value of the following function over the given inte

Question

please help

Find the average value of the following function over the given interval. Draw a graph of the function and indicate the average value. f(x) =x(x - 1); [3,7] The average value of the function is f = . What is the average distance between the parabola y = 7x(16 - x) and the x-axis on the interval [0,16]? The average distance is . (Type an integer, proper fraction or mixed number.) The height of an arch above the ground is given by the function y = 9 cos x for - pi/2 x pi/2. What is the average height of the arch above the ground? The average height is . (Type an exact answer, using pi as needed.)

Explanation / Answer

Q1.average value=(integral of f(x)*dx with the given limit)/total interval

=[x(x-1)*dx , with x=3 to x=7]/(7-3)

=[(x^2/2)-x with x=3 to x=7]/(4)

=16/4=4

Q2.average distance =(y-x)*dx /(16-0)

=290.6

Q3.average distance=y*dx/((pi/2)-(-pi/2))

=5.73

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