Question

The value of dx, where [ . ] represents the greatest integer function is -

• A. p
• B. 2p
• C. –p
• D. 2p/3

Answer 1

Answer: (D)

2p/3

Answer 2

$\int _ { 0 } ^ { \pi } [ 2 \sin x ]$ dx

= $\int _ { 0 } ^ { \pi / 6 } [ 2 \sin x ] d x$ +

+ $\int _ { \pi / 2 } ^ { 5 \pi / 6 } [ 2 \sin x ] d x$ + $\int _ { 5 \pi / 6 } ^ { \pi } [ 2 \sin x ] d x$

= $\int _ { 0 } ^ { \pi / 6 } 0 \mathrm { dx }$ + $\int _ { \pi / 6 } ^ { \pi / 2 } 1 \mathrm { dx }$ ++

= $\frac { \pi } { 2 }$ – $\frac { 5 \pi } { 6 }$ – $\frac { \pi } { 2 }$ = $\frac { 2 \pi } { 3 }$.