The area of the region bounded by the curve y | vedclass

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Question

(C) The area $A$ is given by the definite integral of the function $y = |x-5|$ from $x=5$ to $x=6$. Since $x \ge 5$ in the interval $[5, 6]$,we have $

Vedclass · Accepted Answer

$0.5$

Vedclass · Answer

(C) The area $A$ is given by the definite integral of the function $y = |x-5|$ from $x=5$ to $x=6$. Since $x \ge 5$ in the interval $[5, 6]$,we have $|x-5| = x-5$. Therefore,$A = \int_{5}^{6} (x-5) \, dx$. Let $u = x-5$,then $du = dx$. When $x=5, u=0$ and when $x=6, u=1$. $A = \int_{0}^{1} u \, du = \left[ \frac{u^2}{2} \right]_{0}^{1} = \frac{1}{2} - 0 = 0.5$ sq. units. Thus,the correct option is $C$.

The area of the region bounded by the curve $y=|x-5|$,the $X$-axis,and the lines $x=5$ and $x=6$ is . . . . . . sq. units.

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