Q73.If [x] denotes the greatest integer less than or equal to x, then the value of the integral ∫π/2−π/2[[x] −sin x]dx is equal to: (1) −π (2) π (3) 0 (4) 1
What This Question Tests
This question tests the understanding of the greatest integer function and properties of definite integrals, particularly for symmetric limits. It requires splitting the integral based on the definition of [x] and evaluating each part.
Concepts Tested
Formulas Used
∫[-a,a] f(x) dx = ∫[0,a] (f(x) + f(-x)) dx
📚 NCERT Sections This Tests
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14.2 Which of the statements given in Exercise 14.1 is true for p-type semiconductos.
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📋 Question Details
- Chapter
- Definite Integration & Area
- Topic
- Properties of definite integrals and greatest integer function
- Year
- 2021
- Shift
- 20 Jul Shift 2
- Q Number
- Q73
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 7: Integrals
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