Q76.If the value of the integral ∫50 x+[x]ex−[x] greatest integer less than or equal to x; then the value of (α + β)2 is equal to : (1) 25 (2) 100 (3) 36 (4) 16
What This Question Tests
This question requires splitting the integral based on integer values of x to handle the greatest integer function and then evaluating a series of simpler definite integrals involving exponential functions.
Concepts Tested
Formulas Used
x = [x] + {x}
∫ e^x dx = e^x
∫(a+x)e^x dx = (a+x-1)e^x
📚 NCERT Sections This Tests
12.5 — A Hydrogen Atom Initially In The Ground Level Absorbs A Photon,
Physics Class 12 · Chapter 12
12.5 A hydrogen atom initially in the ground level absorbs a photon, which excites it to the n = 4 level. Determine the wavelength and frequency of photon.
3.26 — The Decomposition Of Hydrocarbon Follows The Equation
Chemistry Class 11 · Chapter 3
3.26 The decomposition of hydrocarbon follows the equation k = (4.5 × 1011s–1) e-28000K/T Calculate Ea. 87 Chemical Kinetics Reprint 2025-26
13.2 — Obtain The Binding Energy Of The Nuclei 5626Fe And 20983 Bi In Units Of
Physics Class 12 · Chapter 13
13.2 Obtain the binding energy of the nuclei 5626Fe and 20983 Bi in units of MeV from the following data: m ( 5626Fe ) = 55.934939 u m ( 20983 Bi ) = 208.980388 u
📋 Question Details
- Chapter
- Definite Integration & Area
- Topic
- Definite integrals with greatest integer function
- Year
- 2021
- Shift
- 26 Aug Shift 2
- Q Number
- Q76
- Type
- Numerical
- NCERT Ref
- Class 12 Mathematics Ch 7: Integrals
More from this Chapter
Q96.Let I = ∫10 sin√xx dx and J = ∫10 cos√xx (1) I > 32 and J > 2 (2) I < 23 and J < 2 (3) I < 32 and J > 2 (4) I > 23 and J < 2
Q97.The area of the plane region bounded by the curves x + 2y2 = 0 and x + 3y2 = 1 is equal to (1) 5 (2) 1 3 3 (3) 2 (4) 4 3 3
Q84.The area of the region bounded by the parabola (y −2)2 = x −1, the tangent to the parabola at the point (2, 3) and the x-axis is (1) 3 (2) 6 (3) 9 (4) 12 JEE Main 2009 JEE Main Previous Year Paper
Q85.The differential equation which represents the family of curves y = c1ec2x , where c1 and c2 are arbitrary constants is (1) y′ = y2 (2) y′′ = y′y (3) yy′′ = y′ (4) yy′′ = (y′)2