Definite Integration questions
424 published questions with worked solutions.
- If f: R R is a differentiable function and f(2) = 6, then _ x 2 _6^ f(x) 2t ,dt (x-2) is:
- The value of the integral _0^1 x ^ -1 (1 - x^2 + x^4) ,dx is:
- The value of _0^ 2 [ 2x(1 + 3x)] ,dx, where [t] denotes the greatest integer function is:
- The value of _0^ | x|^3 ,dx is:
- If _0^ /2 x x + x dx = m( + n), then m · n is equal to:
- _ n ( n n^2 + 1^2 + n n^2 + 2^2 + n n^2 + 3^2 + + 1 5n ) is equal to:
- Let f and g be continuous functions on [0, a] such that f(x) = f(a − x) and g(x) + g(a − x) = 4, then _0^af(x)g(x)dx is equal to:
- The integral _ /6 ^ /3 dx 2x( ^5x + ^5x) equals:
- The value of the integral _ -2 ^ 2 ^2x [ x ] + 12 dx (where [x] denotes the greatest integer less than or equal to x) is:
- The value of _ - /2 ^ /2 dx [x] + [ x] + 4 , where [t] denotes the greatest integer less than or equal to t, is:
- If _0^xf(t) ,dt = x^2 + _x^1t^2f(t) ,dt, then f' ( 12 ) is:
- The value of for which 4 _ -1 ^ 2 e^ - |x| dx=5, is:
- The value of _0^ 2 x ^8 x ^8 x+ ^8 x dx is equal to
- If for all real triplets (a, b, c), f(x)=a+bx+cx^2; then _0^1 f(x) ,dx is equal to :
- The value of _0^1(2x^3 - 3x^2 - x + 1)^3dx is equal to:
- Let f : (0, ∞) → R and F(x) = _0^xtf(t)dt. If F(x^2) = x^4 + x^5, then _ r=1 ^ 12 f(r^2) is equal to __________ .
- The value of the integral _0^ /4 x ,dx ^4(2x) + ^4(2x) equals:
- If _ - /2 ^ /2 8 2 x ,dx (1 + e^ x )(1 + ^4x) = + _e(3 + 2 2) where α, β are integers, then α² + β² equals_____.
- If the value of the integral _ -1 ^ 1 x 1 + 3^x dx is 2 . Then, a value of α is
- Let f(x) = cases -2, & -2 x 0 x - 2, & 0 < x 2 cases and h(x) = f(|x|) + |f(x)|. Then _ -2 ^ 2 h(x) ,dx is equal to-
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