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

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Question

(D) The given curve is $y = |x - 3|$.For the interval $x \in [0, 2]$,the expression $(x - 3)$ is always negative,so $|x - 3| = -(x - 3) = 3 - x$.The a

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(D) The given curve is $y = |x - 3|$.For the interval $x \in [0, 2]$,the expression $(x - 3)$ is always negative,so $|x - 3| = -(x - 3) = 3 - x$.The area $A$ is given by the integral $\int_{0}^{2} (3 - x) \, dx$.Evaluating the integral: $A = [3x - \frac{x^2}{2}]_{0}^{2}$.Substituting the limits: $A = (3(2) - \frac{2^2}{2}) - (3(0) - \frac{0^2}{2})$.$A = (6 - 2) - 0 = 4$ sq. units.Therefore,the correct option is $D$.

The area of the region bounded by the curve $y=|x-3|$,the $X$-axis,and the lines $x=0$ and $x=2$ is . . . . . . sq. units.

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