Definite Integration questions
424 published questions with worked solutions.
- Let f(x) and g(x) be two functions satisfying f(x^2)+g(4-x)=4x^3 and g(4-x)+g(x)=0, then the value of _ -4 ^4f(x)^2dx is
- If [x] denotes the greatest integer less than or equal to x, then the value of the integral _ - /2 ^ /2 [[x]- x]dx is equal to -
- If f : R R is given by f(x) = x + 1, then the value of _ n 1 n [f(0)+f ( 5 n )+f ( 10 n )+ +f ( 5(n-1) n ) ] is
- Let g(T) = _ - /2 ^ /2 ( 4 t+f(x) )dx, where f(x)= _e(x+ x^2+1 ), x R. Then which one of the following is correct?
- The value of the integral _ -1 ^1 _e( 1-x + 1+x )dx is equal to :
- If _0^ 100 ^2x e^ ( x - [ x ] ) dx= ^3 1+4 ^2 , R where [x] is the greatest integer less than or equal to x, then the value of is...
- The value of the integral, _1^3[x^2-2x-2]dx where [x] denotes the greatest integer less than or equal to x, is :
- Let f(x) be a differentiable function defined on [0, 2] such that f'(x) = f'(2–x) for all x (0,2), f(0)=1 and f(2) = e^2. Then...
- If _ -a ^0(|x|+|x-2|)dx=22, (a > 2) and [x] denotes the greatest integer x, then _a^ -a (x+[x])dx is equal to ———
- The value of _ n 1 n _ j=1 ^n (2j-1)+8n (2j-1)+4n is equal to :
- The value of the definite integral _ /4 ^ /4 dx (1+e^ x x )( ^4x+ ^4x) is equal to :
- Let the domain of the function f(x)= _4( _5( _3(18x-x^2-77))) be (a, b). Then the value of the integral _a^b ^3x ( ^3x+...
- Let F : [3, 5] R be a twice differentiable function on (3, 5) such that F(X)=e^ -X _3^x(3t^2+2t+4F'(t))dt. If F'(4)= e^ -224 (e^...
- _6^ 16 _ex^2 _ex^2+ _e(x^2-44x+484) dx is equal to :
- Let f be a non-negative function in [0, 1] and twice differentiable in (0, 1). If _0^x 1-(f'(t))^2 dt= _0^xf(t)dt, 0 1 and f(0) =...
- Let [t] denote the greatest integer . Then the value of 8. _ 1/2 ^1([2x]+|x|dx) is _______
- If x (x) = _5^x(3t^2-2 '(t))dt, x > –2, and (0) = 4, then (2) is_____.
- _ n [ 1 n + n (n+1)^2 + n (n+2)^2 + ..+ n (2n-1)^2 ] is equal to :
- The value of the integral _ -1 ^1 (x+ x^2+1 )dx is :
- The value of the definite integral _ /24 ^ 5 /24 ( 2x)^ 1/3 ( 2x)^ 1/3 +( 2x)^ 1/3 dx is :
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