Question

T`he area bounded by the graph y = |[x – 3]| the x-axis and the lines x = –2 and x = 3 is ([.] denotes the greatest integer function) -

• A. 7 sq. units
• B. 15 sq. units
• C. 21 sq. units
• D. 28 sq. units

Answer 1

Answer: (B)

15 sq. units

Answer 2

\ Required area

= $\int _ { - 2 } ^ { 3 } | [ x - 3 ] |$ dx = $\int _ { - 2 } ^ { - 1 } | [ x - 3 ] |$ dx + $\int _ { - 1 } ^ { 0 } | [ x - 3 ] |$dx +

dx + $\int _ { 1 } ^ { 2 } | [ x - 3 ] |$dx + $\int _ { 2 } ^ { 3 } | [ x - 3 ] |$ dx = $\int _ { - 2 } ^ { - 1 } 5$dx + $\int _ { - 1 } ^ { 0 } 4$. dx +

+ + = 5(1) + 4(1) + 3(1) + 2(1) +1(1)

= 15 sq. units.