The area of the region described by A={(x,y):x2+y2≤1andy2≤1−x} is :
A
π2+43
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B
π2−43
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C
π2−23
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D
π2+23
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Solution
The correct option is Aπ2+43 Required area =P+Q
Now, area of the region P=12×π×(1)2=π2
Now, area of the region Q=∣∣
∣∣21∫0√1−xdx∣∣
∣∣ =∣∣
∣
∣∣2(1−x)3/232⋅(−1)∣∣
∣
∣∣10 =∣∣∣−43∣∣∣ =43
Hence, Required area =π2+43