The area of the region bounded by the curves | vedclass

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(A) The given curves are $y = |x - 4|$,$x = 3$,$x = 5$,and the $X$-axis $(y = 0)$.We know that $|x - 4| = x - 4$ if $x \ge 4$ and $-(x - 4)$ if $x < 4

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(A) The given curves are $y = |x - 4|$,$x = 3$,$x = 5$,and the $X$-axis $(y = 0)$.We know that $|x - 4| = x - 4$ if $x \ge 4$ and $-(x - 4)$ if $x The area $A$ is given by the integral $\int_{3}^{5} |x - 4| \, dx$.Splitting the integral at $x = 4$:$A = \int_{3}^{4} -(x - 4) \, dx + \int_{4}^{5} (x - 4) \, dx$$A = \int_{3}^{4} (4 - x) \, dx + \int_{4}^{5} (x - 4) \, dx$Evaluating the first integral: $[4x - \frac{x^2}{2}]_{3}^{4} = (16 - 8) - (12 - 4.5) = 8 - 7.5 = 0.5$.Evaluating the second integral: $[\frac{x^2}{2} - 4x]_{4}^{5} = (12.5 - 20) - (8 - 16) = -7.5 - (-8) = 0.5$.Total area $A = 0.5 + 0.5 = 1$ square unit.

The area of the region bounded by the curves $y = |x - 4|$,$x = 3$,$x = 5$,and the $X$-axis is

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