Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main202529 Jan 2025Morning ShiftMathematicsDefinite IntegrationActual

The integral (80 ₀^ 4 ( + 9+16 2 ) d ) is equal to :

Options

  1. A(3 _e 4 )
  2. B(4 _ e 3 )
  3. C(6 _e 4 )
  4. D(2 _e 3 )

Correct answer

B. (4 _ e 3 )

Step-by-step solution

aligned & I= ₀^ 4 ( + 9-16 2 ) d & Take - =t & ( + ) d =d t & ( - )^2=t^2 & 2 =1-t^2 & =0 t=-1 & = 4 t=0 & I= _ -1 ^0 d t 9+16 (1-t^2 ) & = 1 16 _ -1 ^0 d t 25 16 16 -t^2 & = 1 4 [ 1 10 _ , 5+4 t . ^ 5-4 t ]_ -1 ^0 & = 1 40 [0+ _e 9 ] & I= _e 9 40 & 80 I=2 _e 9 & 80 I=4 _e 3 aligned

Practice Definite Integration on Quantrex Academy →

More from Definite Integration

The value of the definite integral ₀² 1 3^ x+3 2 , dx is 2026The value of the integral ₀² x(x^2+x+1) ( x+1 )( x^4+x^2+1 ) , dx is equal to: 2026If _ /6 ^ /4 ( (x- 3 ) (x+ 3 )+1 )dx = _e( 3 -1) , then 9 ^2 is equal to ________. 2026Let A = bmatrix 1 & 3 & -1 2 & 1 & 0 & 1 & -1 bmatrix be a singular matrix. Let f(x) = ₀^x (t^2 + 2t + 3) ,dt , x [1, ] . If M and m are respectively the maximum and the minimum va 2026Let f: R R be such that f(xy) = f(x)f(y) , for all x, y R and f(0) 0 . Let g: [1, ) R be a differentiable function such that x^2 g(x) = ₁^x (t^2 f(t) - tg(t)) ,dt . Then g(2) is eq 2026The value of the integral _ -1 ¹ ( x^3 + |x| + 1 x^2 + 2|x| + 1 ) dx is equal to : 2026The value of the integral _ - /4 ^ /4 ( 32 ^4 x 1 + e^ x )dx is: 2026Let (2^ 1-a + 2^ 1+a ) , f(a) , (3^a + 3^ -a ) be in A.P. and be the minimum value of f(a) . Then the value of the integral _ _e( -1) ^ _e( ) dx (e^ 2x - e^ -2x ) is : 2026 Full Definite Integration list All JEE Main PYQs