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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Area Under Curves

NDA 2021 · Mathematics · Area Under Curves

What is the area bounded by y=[x] , where [·] is the greatest...

What is the area bounded by y=[x]y=[x], where [⋅][\cdot] is the greatest integer function, the xx-axis and the lines x=−1.5x=-1.5 and x=−1.8x=-1.8 ?

Options

  1. A0.3 square unit
  2. B0.4 square unit
  3. C0.6 square unit
  4. D0.8 square unit

Correct answer

C. 0.6 square unit

Step-by-step solution

Given y=[x] and x=−1.5,x=−1−8x=-1.5, x=-1-8 Here ∫−1.8−1.5[x]dx=∫−1.8−1.5−2dx=−2[x]−1.8−1.5=−2[−1.5+1.8]=−0.6=0.6 square unit. \begin{aligned} & \text{ Here } \int_{-1.8}^{-1.5}[x] d x=\int_{-1.8}^{-1.5}-2 d x=-2[x]_{-1.8}^{-1.5} \\ & =-2[-1.5+1.8] \\ & =-0.6 \\ & =0.6 \text{ square unit. } \end{aligned}$$
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