A) 2 sq. unit
B) 3 sq. unit
C) 4 sq. unit
D) None of these
Correct Answer: C
Solution :
[c] We have, \[0\le \frac{{{x}^{2}}}{64}<1,\] if \[-8<x<8\] \[\Rightarrow 2\le \frac{{{x}^{2}}}{64}+2<3,\,\,if\,\,\left| x \right|<8\] \[\Rightarrow y=\left[ \frac{{{x}^{2}}}{64}+2 \right]=2,\] if \[\left| x \right|<8\] The graphs of the given curves is as shown in figure. Req. area = area of the shaded region \[=\int_{0}^{2}{xdy}\] \[=\int_{0}^{2}{(y+1)dy=\frac{1}{2}\left[ {{(y+1)}^{2}} \right]_{0}^{2}=\frac{9}{2}-\frac{1}{2}=4}\] sq. unit.You need to login to perform this action.
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