Let y = g ( x ) be the inverse of a bijective mapping f : R → R defined as f ( x ) = 3 x 3 + 2 x . The area bounded by the graph of g ( x ) , the x -axis and the coordinate at x = 5 is ' A '

Question

Let y = g ( x ) be the inverse of a bijective mapping f : R → R defined as f ( x ) = 3 x 3 + 2 x . The area bounded by the graph of g ( x ) , the x -axis and the coordinate at x = 5 is ' A ' then the value of ( 4 A − 7 ) is

TestHub · Accepted Answer

The inverse of y = 3 x 3 + 2 x is x = 3 y 3 + 2 y . The required area is: A = ∫ 0 1 ​ ( 5 − ( 3 y 3 + 2 y ) ) d y = [ 5 y − ( 4 3 y 4 ​ + y 2 ) ] 0 1 ​ = 5 − ( 4 3 ​ + 1 ) = 4 20 − 7 ​ = 4 13 ​ Thus, 4 A = 13 . Therefore, 4 A − 7 = 6 .

Mathematics - Area Under Curves Question with Solution | TestHub

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