Definite Integration questions
424 published questions with worked solutions.
- Let f be a real-valued function defined on the interval (0, ) by f(x) = n , x + _0^x 1 + t ; dt. Then which of the following...
- Let f : [1, ) [2, ) be a differentiable function such that f(1) = 2. If 6 _1^x f(t) ,dt = 3x ,f(x) - x^3 for all x 1, then the...
- Let f : [-1, 2] [0, ) be a continuous function such that f(x) = f(1 - x) for all x [-1, 2]. Let R_1 = _ -1 ^ 2 x f(x) ,dx, and...
- The value of the integral _ - /2 ^ /2 (x^2 + + x - x ) x ,dx is
- For a R (the set of all real numbers), a ≠ −1, _ n (1^a + 2^a + + n^a) (n + 1)^ a-1 [(na + 1) + (na + 2) + + (na + n) ] = 1 60...
- Let f : (0, ∞) → ℝ be given by f(x) = _ 1 x ^ x e^ - (t + 1 t ) dt t . Then
- List I P. The number of polynomials f(x) with non-negative integer coefficients of degree ≤ 2, satisfying f(0) = 0 and _0^1f(x)...
- Let f: R R be a function defined by f(x)= cases [x], & x 2 0, & x>2 cases , where [x] is the greatest integer less than or equal...
- The option(s) with the values of a and L that satisfy the following equation is(are) _0^ 4 e^t( ^6at+ ^4at) ,dt _0^ e^t( ^6at+...
- The total number of distinct x [0,1] for which _0^x t^2 1+t^4 ,dt=2x-1 is
- The value of _ - 2 ^ 2 x^2 x 1+e^x ,dx is equal to
- For each positive integer n, let y_n= 1 n ((n+1)(n+2) (n+n) )^ 1 n . For x R , let [x] be the greatest integer less than or equal...
- If I= 2 _ - /4 ^ /4 dx (1+e^ x )(2- 2x) then 27I^2 equals _____
- For a R , |a|>1, let _ n ( 1+ [3] 2 + + [3] n n^ 7/3 ( 1 (an+1)^2 + 1 (an+2)^2 + + 1 (an+n)^2 ) )=54. Then the possible value(s)...
- The value of the integral _0^ /2 3 ( + )^5 ,d equals _____
- Let f(x) be a function such that f' ( 1 x )+x^3f'(x)=0. What is _ -1 ^ 1 f(x) ,dx equal to?
- What is _ 1 ^ 3 |1-x^4| ,dx equal to?
- If f(x) and g(x) are continuous functions satisfying f(x)=f(a-x) and g(x)+g(a-x)=2, then what is _ 0 ^ a f(x)g(x) ,dx equal to?
- What is _ e^ -1 ^ e^2 | x x |dx equal to?
- What is _ 0 ^ 2 [x^2] ,dx equal to (where [.] is the greatest integer function)?
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