int_{0}^{4}|x-2| d x= | vedclass

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(B) We need to evaluate the definite integral $\int_{0}^{4}|x-2| d x$.The function $|x-2|$ changes its definition at $x=2$. Specifically,$|x-2| = -(x-

Vedclass · Accepted Answer

$4$

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(B) We need to evaluate the definite integral $\int_{0}^{4}|x-2| d x$.The function $|x-2|$ changes its definition at $x=2$. Specifically,$|x-2| = -(x-2) = 2-x$ for $x Thus,we split the integral at $x=2$:$\int_{0}^{4}|x-2| d x = \int_{0}^{2}(2-x) d x + \int_{2}^{4}(x-2) d x$Evaluating the first part: $\int_{0}^{2}(2-x) d x = [2x - \frac{x^2}{2}]_{0}^{2} = (4 - 2) - (0 - 0) = 2$.Evaluating the second part: $\int_{2}^{4}(x-2) d x = [\frac{x^2}{2} - 2x]_{2}^{4} = (8 - 8) - (2 - 4) = 0 - (-2) = 2$.Adding the two parts: $2 + 2 = 4$.

$\int_{0}^{4}|x-2| d x=$

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