JEE Main201815 Apr 2018Morning ShiftMathematicsIndefinite IntegrationActual

If f ( x-4 x+2 )=2 x+1,(x R= 1,-2 ) , then f ( x ) d x is equal to (where C is a constant of integration)

Options

A12 _e|1-x|-3 x+c
B-12 _e|1-x|-3 x+c
C-12 _e|1-x|+3 x+c
D12 _e|1-x|+3 x+c

Correct answer

B. -12 _e|1-x|-3 x+c

Step-by-step solution

Suppose, x-4 x+2 =y x-4=y(x+2) x(1-y)=2 y+4 x= 2 y+4 1-y So, f(y)=2 ( 2 y+4 1-y )+1 Now, f(x)=2 ( 2 x+4 1-x )+1= 3 x+9 1-x aligned &= 3(x+3) 1-x = 3(x-1+4) 1-x =-3+ 12 1-x & f(x) d x=-12 _e|1-x|-3 x+c aligned

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