What is the integral from 1 to 7 of (12-|x-4|)^2 ?

The integral from 1 to 7 of (12-|x-4|)^2 is 666

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integral from 1 to 7 of (12-|x-4|)^2

\int_{1}^{7} (12 - ∣ x - 4 ∣)^{2} d x

666

Solution steps

\int_{1}^{7} (12 - ∣ x - 4 ∣)^{2} d x

Eliminate Absolutes

= \int_{1}^{4} (12 - (- x + 4))^{2} d x + \int_{4}^{7} (12 - (x - 4))^{2} d x

\int_{1}^{4} (12 - (- x + 4))^{2} d x = 333

\int_{4}^{7} (12 - (x - 4))^{2} d x = 333

= 333 + 333

Simplify

= 666

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What is the integral from 1 to 7 of (12-|x-4|)^2 ?
The integral from 1 to 7 of (12-|x-4|)^2 is 666