(D) The given curve is $y = |x - 5|$.Since the interval is $x \in [0, 2]$,we have $x - 5 < 0$,so $|x - 5| = -(x - 5) = 5 - x$.The area $A$ is given by

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(D) The given curve is $y = |x - 5|$.Since the interval is $x \in [0, 2]$,we have $x - 5 The area $A$ is given by the integral:$A = \int_{0}^{2} (5 - x) \, dx$$A = [5x - \frac{x^2}{2}]_{0}^{2}$$A = (5(2) - \frac{2^2}{2}) - (0 - 0)$$A = 10 - 2 = 8$ sq. units.Thus,the correct option is $D$.

Class 12 Mathematics Application of Integration Area bounded by region of single curve

Easy

The area of the region bounded by the curve $y = |x - 5|$,$y = 0$,$x = 0$,and $x = 2$ is . . . . . . sq. units.

GSEB 2013 All GSEB

A
$9/2$
B
$7/2$
C
$9$
D
$8$

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Application of Integration

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Area bounded by region of single curve

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The area of the region bounded by the curve $y = |x - 5|$,$y = 0$,$x = 0$,and $x = 2$ is . . . . . . sq. units.

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