For each problem, find the average value of the function over the given interval.
Problem 1 :
f(x) = 2x^{2} – 8x + 5; [0, 3]
Solution :
a = 0, b = 3, then b - a = 3 - 0 ==> 3
So, the average value of the given function in the given interval is -1.
Problem 2 :
Solution :
a = 0, b = 1, then b - a = 1 - 0 ==> 1
So, the average value of the given function in the given interval is 3.34.
Problem 3 :
Solution :
a = 0, b = 1, then b - a = 1 - 0 ==> 1
So, the average value of the given function in the given interval is 4 ln 2.
Problem 4 :
f(x) = -x + 1; [-4, 0]
Solution :
a = -4, b = 0, then b - a = 0 + 4 ==> 4
So, the average value of the given function in the given interval is 3.
Problem 5 :
f(x) = 2x + 1; [-4, 0]
Solution :
a = -4, b = 0, then b - a = 0 + 4 ==> 4
So, the average value of the given function in the given interval is -3.
Problem 6 :
f(x) = 2x + 1; [-2, 3]
Solution :
a = -2, b = 3, then b - a = 3 + 2 ==> 5
So, the average value of the given function in the given interval is 2.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
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