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I have a question asking "What is the average value of the function x^2+4x-9 on the interval [-1,7]?" I keep on getting the answer 10 by plugging in -1 for x and getting -12 then plug in 7 for x and you get 68 then doing 68+12/7+1 but the correct answer is 52/3 can someone please help me because I don't understand

Respuesta :

Answer:

The general antiderivative of x² + 4x - 9 is (1/3)x³ + 2x² - 9x.

(1/3)(7³) + 2(7²) - 9(7) = 448/3

(1/3)(-1)³ + 2(-1)² - 9(-1) = 32/3

Average value =

(1/(7 - (-1)))(448/3 - 32/3) =

(1/8)(416/3) = 52/3

See the attachment.

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