Jj M.

asked • 04/12/23

Find the area (in square units) of the region under the graph of the function f on the interval [5, 7].f(x) = 4e^x − x

^^

William W.

Have you learned about integration? Area under the curve is the integration of the function between the two values of x (x = 5 and x = 7). It involves finding the antiderivative (or using a calculator to numerically calculate the answer)
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04/12/23

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William W. answered • 04/12/23

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Area = 4•5∫7ex dx - 5∫7x dx


The antiderivative of ex is ex and the antiderivative of x is x2/2


So the Area = 4•(e7 - e5) - (72/2 - 52/2) ≈ 4•(1096.633 - 148.413) - (49/2 - 25/2) ≈ 4(948.22) - 12 ≈ 3780.88


Or you can just type the problem in your calculator as I have it written and get the same result

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