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Coordinate Planes in Three Dimensional Space

Let [.] denot...

Question

Let $[.]$ denote the greatest integer function. The area (in sq. units) bounded by the curves $y = [\frac{x^{2}}{64} + 2],$ $y = x - 1,$ $x = 0$ above the $x -$ axis is

4.00

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Solution

$y = [\frac{x^{2}}{64} + 2]$
For $- 8 < x < 8$ , we get $y = 2$
Let us draw the figure.

$∴$ Required area
$=$ Area of the trapezium $O A B C$
$= \frac{1}{2} (O A + C B) \cdot O C$
$= \frac{1}{2} (1 + 3) \cdot 2$
$= 4$ sq. units

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