The area bounded by the graph $y = |\lbrack x - 3\rbrack|$, the $x$-axis and the lines $x = - 2$ and $x = 3$ is( $\lbrack.\rbrack$ denotes the greatest integer function)

Question

Dr. Abubacker · Accepted Answer

(b)
Required area $= \int_{- 2}^{3}{\left| \ \lbrack x - 3\rbrack \right|dx}$
$= \int_{- 2}^{- 1}{\left| \ \lbrack x - 3\rbrack \right|dx + \int_{1}^{0}{\left| \lbrack x - 3\rbrack \right|dx}}$
$+ \int_{0}^{1}{\left| \lbrack x - 3\rbrack \right|dx + \int_{1}^{2}{\left| \lbrack x - 3\rbrack \right|dx + \int_{2}^{3}{|\lbrack x - 3\rbrack|dx}}}$
$= \int_{- 2}^{- 1}5 \bullet dx + \int_{- 1}^{0}{4 \bullet dx + \int_{0}^{- 1}{3 \bullet dx + \int_{1}^{2}{2 \bullet dx + \int_{2}^{3}{1 \bullet dx}}}}$
$= 5(1) + 4(1) + 3(1) + 2(1) + 1(1)$
$= 15\ sq\ unit$

Q. The area bounded by the graph $y = |\lbrack x - 3\rbrack|$, the $x$-axis and the lines $x = - 2$ and $x = 3$ is( $\lbrack.\rbrack$ denotes the greatest integer function)

Explanation

Reviewed by Dr. Abubacker

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