If the area of the region { ( x , y ) : x 2 a ≤ y ≤ x 1 , 1 ≤ x ≤ 2 , 0

Question

If the area of the region { ( x , y ) : x 2 a ​ ≤ y ≤ x 1 ​ , 1 ≤ x ≤ 2 , 0 < a < 1 } is ( lo g e ​ 2 ) − 7 1 ​ then the value of 7 a − 3 is equal to:

TestHub · Accepted Answer

​ area ∫ 1 2 ​ ( x 1 ​ − x 2 a ​ ) d x [ ℓ n x + x a ​ ] 1 2 ​ ℓ nn 2 + 2 a ​ − a = lo g e ​ 2 − 7 1 ​ 2 − a ​ = − 7 1 ​ a = 7 2 ​ 7 a = 2 7 a − 3 = − 1 ​

Mathematics - Area Under Curves Question with Solution | TestHub

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