Question

$\int _ { - 1 } ^ { 1 } [ x [ 1 + \sin \pi x ] + 1 ]$ dx is ([·] denotes greatest integer function)

• A. 2
• B. 0
• C. 1
• D. None

Answer 1

Answer: (A)

2

Answer 2

–1 < x < 0 0 < 1 + sin p x < 1

[x [1 + sin p x] + 1] = 1

[1 + sin p x] = 0

0 < x < 1 1 < 1 + sin px < 2

[1 + sin p x] = 1

[x [1 + sin p x] + 1] = 1

$\int _ { - 1 } ^ { 1 } d x$ ̃ 2 = = 2