Find the average value of the function fx 3x2 3 over the i

Find the average value of the function f(x) = 3x^2 - 3 over the interval [0, 1].

Solution

We have f(x) = 3x²-3. The average value of f(x) over the interval [0,1} is 1/(1-0) ¹₀ f(x) dx = ¹₀ (3x²-3 ) dx = [3 (x³/3)-3x+c]¹₀ , where c is an arbitrary constant. Thus, the average value of f(x) over the interval [0,1} is [x³-3x +c]₀¹ = (1)³ -3*1 +c -c = 1-3 = -2.