Integrals · Question 2

JEE Advanced 2025 Paper 2NumericalHard📈 Topic in 50% papers+4

If = 122 -1x2x2-3x+2 dx, then the value of 7 ( 2 7 ) is . (Here, the inverse trigonometric function -1x assumes values in (- 2, 2 ).)

Answer

Solution

Put x 1x: dx - dxx2 and 2x2-3x+2 2-3x+2x2x2, so = 1/22 -1(1/x)2x2-3x+2dx.

Add: 2 = 2 1/22 dx2x2-3x+2 (as -1x+ -1 1x= 2 for x>0).

dx2 [(x- 34)2+ 716 ]= 2 7 -1 4x-3 7; limits give 2 7 [ -1 5 7+ -1 1 7 ]= 2 7 -1(3 7) (since 6/ 71-5/7=3 7).

= 4 2 7 -1(3 7) 2 7 = -1(3 7).

7 ( 2 7 )= 7 3 7=21

Answer: 21

JEE Advanced 2025 Paper 2

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