Q74.Let [t] denote the greatest integer less than or equal to t. Then the value of ∫21 |2x −[3x]|dx is
What This Question Tests
This question tests the ability to evaluate a definite integral involving the greatest integer function and an absolute value, requiring the integral to be split into multiple parts based on the intervals where the functions change their definition.
Concepts Tested
Formulas Used
Definition of [t]
Properties of ∫f(x)dx
📚 NCERT Sections This Tests
14.2 — Which Of The Statements Given In Exercise 14.1 Is True For P-Type
Physics Class 12 · Chapter 14
14.2 Which of the statements given in Exercise 14.1 is true for p-type semiconductos.
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.
1.3 — Define The Following Terms:
Chemistry Class 11 · Chapter 1
1.3 Define the following terms: (i) Mole fraction (ii) Molality (iii) Molarity (iv) Mass percentage.
📋 Question Details
- Chapter
- Definite Integration & Area
- Topic
- Integration of greatest integer function
- Year
- 2020
- Shift
- 02 Sep Shift 2
- Q Number
- Q74
- 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