If the area of the region { ( x , y ) : 4 − x 2 ≤ y ≤ x 2 , y ≤ 4 , x ≥ 0 } is ( α 80 2 ; − β ) , α , β ∈ N , then α + β is equal to _______.

Question

If the area of the region { ( x , y ) : ​ 4 − x 2 ​ ≤ y ≤ x 2 , y ≤ 4 , x ≥ 0 } is ( α 80 2 ​ ​ ; − β ) , α , β ∈ N , then α + β is equal to _______.

TestHub · Accepted Answer

A = ∫ 0 4 ​ 4 + y ​ dy − ∫ 0 2 ​ 4 − y ​ dy − ∫ 2 4 ​ y ​ dy = ( 2 3 ​ ( 4 + y ) 2 3 ​ ​ ) 0 4 ​ + ( 2 3 ​ ( 4 − y ) 2 3 ​ ​ ) 0 2 ​ − ( 2 3 ​ y 2 3 ​ ​ ) 0 4 ​ 3 80 2 ​ ​ − 16 = 3 40 2 ​ ​ − 16 α = 6 , β = 16 α + β = 22

Mathematics - Area Under Curves Question with Solution | TestHub

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