Integrals · Question 48

JEE Main 2025 (Online) 28th January Morning ShiftMCQMedium📈 Topic in 71% papers+4−1

If - 2 2 96x2 2 x(1 + ex) dx = ( 2 + ), , Z, then ( + )2 equals

Answer

(2) 100

Solution

Let I = - 2 2 96x2 2 x1 + ex dx. Using x -x:

I = - 2 2 96x2 2 x ex1 + ex dx

Adding: 2I = - 2 2 96x2 2 x dx = 2 0 2 96x2 2 x dx

I = 48 0 2 x2(1 + 2x) dx

0 2 x2 dx = 324

x2 2x dx = x2 2x2 + x 2x2 - 2x4

0 2 x2 2x dx = 2 (-1)2 = - 4

I = 48 ( 324 - 4 ) = 2 3 - 12 = (2 2 - 12)

= 2, = -12

( + )2 = (-10)2 = 100

Answer: (2)

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