We have <span>y=cos x/(x</span>²+x+2) <span>on the closed interval [-1, 3] </span><span> we know that </span>The average value of f(x) on the interval [a, b] is given by: <span>F(avg) = 1/(b - a) ∫ f(x) dx (from x=a to b). (b-a)=(3+1)------> 4 </span>= 1/4 ∫ cos(x)/(x² + x + 2) dx (from x=-1 to 3).
Note that [cos(x)/(x² + x + 2)] does not have an elementary anti-derivative. By approximating techniques: 1/4 ∫ cos(x)/(x^2 + x + 2) dx (from x=-1 to 3) ≈ 0.182951
the answer is <span>the average value of y = cos(x)/(x</span>²<span> + x + 2) on [-1, 3] is approximately 0.182951</span>
