Since F(x) = 4 + x2 is continuous on the interval (-2, 4], the mean value theorem for integrals says there is a number i

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Since F X 4 X2 Is Continuous On The Interval 2 4 The Mean Value Theorem For Integrals Says There Is A Number I 1 (25.86 KiB) Viewed 20 times

Since F(x) = 4 + x2 is continuous on the interval (-2, 4], the mean value theorem for integrals says there is a number in (-2, 4] such that [ ^4 + x2) dx = ) dx = f(c) [4 - (-2)] In this particular case we can find c explicitly. Using the formula f(x) dx, we find the average value of the function fave = 3, so the value of a satisfies f(c) = fave = 8. b-a Therefore 4 + 2 = so 2 - So in this case there happen to be two numbers c = +2 in the interval (-2, 4] that work in the mean value theorem for integrals. y 20 15 10 Save. = 8 X 2 6