Integrals

JEE Main 2025 (Online) 23rd January Evening ShiftMCQMedium📈 Topic in 66% papers+4−1

Ques. 1JEE Main 2025, 23 January (Evening Shift)

If I= 0 2 32x 32x+ 32x dx, then 02I x x x 4x+ 4x dx equals :

Answer

(3) 216

King's property: x 2-x in I and add 2I= 0 /2dx= 2, so the limits are 0 to 2.

J= 0 /2 x x x 4x+ 4xdx; same property: 2J= 2 0 /2 x x 4x+ 4xdx

Divide by 4x, put t= 2x, dt=2 x 2x dx:

J= 4 12 0 dt1+t2= 8 2

J= 216

Answer: (3)

Ques. 2JEE Main 2025, 23 January (Evening Shift)

Let x3 x dx=g(x)+C, where C is the constant of integration. If 8 (g ( 2 )+g' ( 2 ) )= 3+ 2+ , , , Z, then + - equals :

Ques. 3JEE 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 :

Ques. 4JEE Main 2025, 22 January (Evening Shift)

If x ( x -1x 1-x2+ -1x(1-x2)3/2+ x1-x2 )dx=g(x)+C, where C is the constant of integration, then g ( 12 ) equals :

All JEE Main Mathematics chapters