JEE Main20249 Apr 2024Evening ShiftMathematicsLimitsActual

_ x 2 ( _ x^3 ^ ( / 2)^3 ( (2 t^ 1 / 3 )+ (t^ 1 / 3 ) ) d t (x- 2 )^2 ) is equal to

Options

A5 ^2 9
B9 ^2 8
C11 ^2 10
D3 ^2 2

Correct answer

B. 9 ^2 8

Step-by-step solution

aligned & _ x 2 0- (2 x)+ (x) 3 x^2 2 (x- 2 ) & = _ x 2 - 2 x x+ x 3 x^2 2 (x- 2 ) & = _ x 2 2 x ( 2 -x ) 2 (x- 2 ) + ( 2 -x ) 2 ( 2 -x ) 3 x^2 & = (1(1)+ 1 2 ) 3 ( 2 )^2 & = 9 ^2 8 aligned

Practice Limits on Quantrex Academy →

More from Limits

Let _ x 2 ( (x-2))(rx^2 + (p-2)x - 2p) (x-2)^2 = 5 for some r, p R . If the set of all possible values of q , such that the roots of the equation rx^2 - px + q = 0 lie in (0, 2) , 2026 The value of _ x 0 ( x^2 ^2 x x^2 - ^2 x ) is: 2026 Let f(x) = _ y 0 (1 - (xy)) (xy) y^3 . Then the number of solutions of the equation f(x) = x , x R is : 2026 The product of all possible values of , for which _ x 0 ( 1 - ( x) (( +1)x) (( +2)x) ^2(( +1)x) ) = 2 , is: 2026 If _ x 2 (x^3 - 5x^2 + ax + b) ( x-1 - 1) _e(x-1) = m , then a + b + m is equal to : 2026 The value of _ x 0 _ e ( (e x) (e² x ) (e¹⁰ x ) ) e²-e^ 2 x is equal to 2026 If _ x 0 e ^ ( a -1) x +2 ~b x+( c -2) e ^ -x x x- _ e (1+x) =2 , then a ²+ b ²+ c ² is equal to : 2026 Let [ ] denote the greatest integer function and f(x)= _ n 1 n ³ _ k =1 ^ n [ k ² 3^ x ] . Then 12 _ j =1 ^ f( j ) is equal to _ _ _ _ . 2026 Full Limits list All JEE Main PYQs