The value of I=∫-11xsin⁡(πx)dx is (where [·] denotes the greatest integer function)

Correct answer: (C) 0. I=2 ∫ 0 1 xsin(πx) dx Now, xsin(πx)∈ 0,1 as x∈ 0,1 ∴ xsin(πx) =0 ∴I=2∫010dx=0

Q4 / 116 · NTA Abhyas (JEE Main) 2020 · Mathematics · Definite Integration

The value of $I = \int_{- 1}^{1} [x \sin (π x)] d x$ is (where [·] denotes the greatest integer function)

I = 2 \int_{0}^{1} [x \sin (π x)] d x

Now,

x \sin (π x) \in (0, 1)

x \in (0, 1)

∴ [x \sin (π x)] = 0

∴ I = 2 \int_{0}^{1} 0 d x = 0

Hence, the correct answer is option: 'C'.