Doubts
Sign in
12thPass logo
New chatPYQ LibraryDoubtsRank report
Sign in to see Recents
Sign in to save progress →
Doubts
Sign in

Definite Integration question

2021 · 17 Mar · Shift 2 · Q28
Guest · try one question or challengeGuest · try one question or challenge
  1. PYQ Library
  2. /JEE Main
  3. /Mathematics
  4. /Definite Integration
  5. /2021 · 17 Mar · Shift 2 · Q28

Definite Integration question

2021 · 17 Mar · Shift 2 · Q28

JEE MainMathematicsDefinite IntegrationMCQ+4 / −1
If the integral ∫010[sin⁡2πx]ex−[x]dx=αe−1+βe−12+γ\int_0^{10} {{{[\sin 2\pi x]} \over {{e^{x - [x]}}}}} dx = \alpha {e^{ - 1}} + \beta {e^{ - {1 \over 2}}} + \gamma∫010​ex−[x][sin2πx]​dx=αe−1+βe−21​+γ, where α\alphaα, β\betaβ, γ\gammaγ are integers and [x] denotes the greatest integer less than or equal to x, then the value of α\alphaα+β\betaβ+γ\gammaγ is equal to :
  1. A
    0
  2. B
    10
  3. C
    20
  4. D
    25
PreviousNext

More from Definite Integration

  • Let In​=∫1e​x19(log∣x∣)ndx, where n ∈ N. If (20)I10 = α I9 + β I8, for natural numbers α and β, then α−β equals to ​.2021 · Numerical
  • Let f(x) and g(x) be two functions satisfying f(x2) + g(4 − x) = 4x3 and g(4 − x) + g(x) = 0, then the value of −4∫4​f(x)2dx is2021 · Numerical
  • Let g(x) = ∫0x​f(t)dt, where f is continuous function in [ 0, 3 ] such that 31​≤ f(t) ≤ 1 for all t ∈[0, 1] and 0 ≤ f(t) ≤21​ for all t ∈ (1, 3]. The largest possible interval in which…2021 · MCQ
  • Let P(x) be a real polynomial of degree 3 which vanishes at x = − 3. Let P(x) have local minima at x = 1, local maxima at x = − 1 and −1∫1​P(x)dx = 18, then the sum of all the coefficients of the polynomial P(x) is…2021 · Numerical
  • Let a be a positive real number such that ∫0a​ex−[x]dx=10e−9 where [ x ] is the greatest integer less than or equal to x. Then a is equal to:2021 · MCQ
  • The value of the integral −1∫1​loge​(1−x​+1+x​)dx is equal to:2021 · MCQ
  • If [x] denotes the greatest integer less than or equal to x, then the value of the integral ∫−π/2π/2​[[x]−sinx]dx is equal to :2021 · MCQ
  • If the real part of the complex number (1−cosθ+2isinθ)−1 is 51​ for θ∈(0,π), then the value of the integral ∫0θ​sinxdx is equal to:2021 · MCQ