High School

Suppose that [tex]\int_{2}^{18} f(x) \, dx = 11[/tex]. Determine the value of [tex]\int_{2}^{18} (f(x) - 8) \, dx[/tex].

a) 139
b) 3
c) -139
d) -117
e) 117

Answer :

d.-117 is the value of ∫¹⁸₂ ​(f(x)−8)dx.

The value of ∫¹⁸₂ ​(f(x)−8)dx can be determined by subtracting 8 times the integral of f(x) from 2 to 18 from 2 to 18 of f(x).

Given that ∫¹⁸₂ ​f(x)dx = 11, we can calculate:

∫¹⁸₂ ​(f(x)−8)dx = ∫¹⁸₂ ​f(x)dx - 8*(18-2) = 11 - 8*16 = 11 - 128 = -117.

Therefore, the value of ∫¹⁸₂ ​(f(x)−8)dx is -117.

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