The value of the integral (where [x] denotes the greatest integer less than or equal to x) is:

Engineering

Mathematics

Introduction to Functions

Modulus Function

Introduction to Definite Integral

Question

The value of the integral $I = \int_{- 2}^{2} \frac{\sin^{2} xdx}{[\frac{x}{π}] + \frac{1}{2}}$ (where [x] denotes the greatest integer less than or equal to x) is:

4 – sin 4

sin 4

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$I = \int_{- 2}^{2} \frac{\sin^{2} x dx}{[\frac{x}{π}] + \frac{1}{2}}$

$I = \int_{- 2}^{2} \frac{\sin^{2} x dx}{- [\frac{x}{π}] - \frac{1}{2}} \Rightarrow 2 I = 0 \Rightarrow I = 0$