Ques. 1JEE Main 2025, 22 January (Morning Shift)
Let for f(x)=7 8x+7 6x-3 4x-3 2x, I1= 0 /4f(x) dx and I2= 0 /4x f(x) dx. Then 7I1+12I2 is equal to :
- 2
- 1
- 2
Answer
(2) 1
Solution
f(x)=(7 6x-3 2x) 2x; put t= x to get f dx= 7x- 3x=F(x).
F(0)=F ( 4 )=0 I1=0
I2= [xF(x) ]0 /4- 0 /4F dx
7x- 3x= 3x( 2x-1) 2x
I2=0- 01(t5-t3) dt
= 14- 16= 112
7I1+12I2=1
Answer: (2)