The area bounded by the loop of 4y2=x24−x2 is

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answer is 0005.33.

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Detailed Solution

4y2=x24−x2−−−(i)⇒y=12x24−x2⇒y=x24−x2∴ Area (A)=4×∫02 2x2×24−x2dx Put 4−x2=t⇒−2xdx=dt∴A=−44∫40 tdt=∫04 tdt=t3/23/204=23×[64−0]⇒A=163 sq.units

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