Definite Integration questions
424 published questions with worked solutions.
- If f(x) = e^x 1 + e^x , I_1 = _ f(-a) ^ f(a) x g x(1-x) ,dx and I_2 = _ f(-a) ^ f(a) g x(1-x) ,dx then the value of I_2/I_1 is
- Let f(x) be a continuous function such that f(x + 4) = f(x + 2) - f(x) and (x) = _x^ x+12 f(x) ,dx. If (3) = 5 then _4^ 16 f(x)...
- Let g(x) = _0^ x f(t) , dt, where 12 f(t) 1 for t [0, 1] and 0 f(t) 12 for t (1, 2]. Then
- If f(x) = cases e^ x x & for |x| 2 2 & otherwise cases then _ -2 ^ 3 f(x) , dx is equal to
- Let f: (0, + ) R and F(x) = _0^x f(t) ,dt. If F(x^2) = x^2(1+x) then f(4) equals
- The value of _ - ^ ^2 x 1 + a^x ,dx (a > 0) is
- Let f(x) = _1^x 2 - t^2 ,dt. Then real roots of the equation x^2 - f'(x) = 0 are
- Let T > 0 be a fixed number. Suppose f is a continuous function such that for all x R, f(x + T) = f(x). If I = _0^T f(x) ,dx then...
- The integral _ -1/2 ^ 1/2 [x] + ( 1+x 1-x ) dx equals
- Let f be a non-negative function defined on the interval [0, 1]. If _0^x 1 - f'(t) ^2 ,dt = _0^x f(t) ,dt, 0 x 1 and f(0) = 0 then
- If I_n = _ - ^ nx (1 + ^x) x ,dx, n = 0, 1, 2, , then
- Let f : R R be a continuous function which satisfies f(x) = _0^x f(t) ,dt. Then the value of f( _e 5) is
- The value of _ x 0 1 x^3 _0^x t (1+t) t^4+4 ,dt is
- Let f be a real-valued function defined on the interval (0, ) by f(x) = _e x + _0^x 1 + t ,dt. Which of the following...
- For any real number x, let [x] = largest integer less than or equal to x. Let f be a real valued function defined on the interval...
- The value of _ 2 ^ 3 x x^2 x^2 + ( 6 - x^2) ,dx is
- 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 - 5 for all x 1 then the...
- The integral _2^4 x^2 x^2 + (6-x)^2 dx is equal to
- For x > 0, let f(x) = _1^x t 1+t ,dt. Then f(x) + f ( 1x ) is equal to
- Let f : R R be a function such that f(2-x) = f(2+x) and f(4-x) = f(4+x), for all x R and _0^2 f(x) ,dx = 5. Then the value of _...
Other chapters
Alcohols, Phenols and EthersAldehydes, Ketones and Carboxylic AcidsAlternating CurrentAminesAnatomy of Flowering PlantsAncient Indian HistoryAnimal KingdomApplication of DerivativesArea Under CurveAromatic Compounds and Aryl HalidesAtomsBasic Mathematics and LogarithmBinomial TheoremBiodiversity and ConservationBiological ClassificationBiomoleculesBiotechnology and Its ApplicationsBiotechnology: Principles and ProcessesBody Fluids and CirculationBreathing and Exchange of GasesCell Cycle and Cell DivisionCell: The Unit of LifeChemical Bonding and Molecular StructureChemical Coordination and Integration