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The area bounded by the curve y=[x^2/64+...

The area bounded by the curve `y=[x^2/64+2],y=x-1,y=x-1 and x=0` above the x-axis will be-(Where [] represents greatest integer function)

A

2

B

3

C

4

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
We have,
`0le(x^(2))/(64)lt1, if -1ltxlt8`
`implies2le(x^(2))/(64)+2lt3,if |x|lt8`
`impliesy=[(x^(2))/(64)+2]=2, if |x|lt8`
The graphs of the given curves is as shown in Fig. 6.

Let required area be A. Then,
A= Area of the shaded region
`impliesA=underset(0)overset(2)(int)xdy=underset(0)overset(2)(int)(y+1)dy`
`impliesA=1/2[(y+1)^(2)]_(0)^(2)=9/2-1/2=4` sq. units.
ALITER The required area A is given by
A=Area of trapezium OABC
`impliesA=1/2(OA+BC)xxOC=1/2(1+3)xx2=4` sq. units
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