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Solution


Q.

Let the area of the region {(x,y):2y≤x2+3, y+|x|≤3, y≥|x–1|} be A. Then 6A is equal to :           [2025]
1 14  
2 16  
3 18  
4 12  

Ans.

(1)

Required area, A = Rectangle ABDE – Area of region EDC

⇒ A=4–2∫01((3–x)–(x2+32))dx

⇒ A=4–2{3x–x22–x36–32x}01

⇒ A=4–2{3–12–16–32}=73

So, 6A = 14.