The value of int_{0}^{8} |x - 5| , dx is | vedclass

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(A) We need to evaluate the definite integral $I = \int_{0}^{8} |x - 5| \, dx$. Since the integrand $|x - 5|$ changes its definition at $x = 5$,we spl

Vedclass · Accepted Answer

$17$

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(A) We need to evaluate the definite integral $I = \int_{0}^{8} |x - 5| \, dx$. Since the integrand $|x - 5|$ changes its definition at $x = 5$,we split the integral at $x = 5$: $I = \int_{0}^{5} -(x - 5) \, dx + \int_{5}^{8} (x - 5) \, dx$. Evaluating the first part: $\int_{0}^{5} (5 - x) \, dx = [5x - \frac{x^2}{2}]_{0}^{5} = (25 - \frac{25}{2}) - 0 = \frac{25}{2} = 12.5$. Evaluating the second part: $\int_{5}^{8} (x - 5) \, dx = [\frac{x^2}{2} - 5x]_{5}^{8} = (\frac{64}{2} - 40) - (\frac{25}{2} - 25) = (32 - 40) - (12.5 - 25) = -8 - (-12.5) = 4.5$. Adding both parts: $I = 12.5 + 4.5 = 17$.

The value of $\int_{0}^{8} |x - 5| \, dx$ is

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