JEE Main20248 Apr 2024Morning ShiftMathematicsIndefinite IntegrationActual

Let I(x)= 6 ^2 x(1- x)^2 d x . If I(0)=3 , then I ( 12 ) is equal to

Options

A2 3
B3
C3 3
D6 3

Correct answer

C. 3 3

Step-by-step solution

I(x)= 6 d x ^2 x(1- x)^2 = 6 cosec ^2 x d x (1- x)^2 Put 1- x=t cosec ^2 xdx = dt aligned & I= 6 d t t^2 = -6 t +c & I(x)= -6 1- x c, c=3 & I(x)=3- 6 1- x , I ( 12 )=3- 6 1-(2+ 3 ) & I ( 12 )=3+ 6 3 +1 =3+ 6( 3 -1) 2 =3 3 aligned

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