Question

The value of dx, where [x] denotes the greatest integer less than or equal to x is –

• A. 5
• B. 7
• C. 4
• D. 3

Answer 1

Answer: (B)

7

Answer 2

dx = dx

+ $\int _ { 1 } ^ { 2 } \{ | \mathrm { x } - 2 | + [ \mathrm { x } ] \} \mathrm { dx }$+$\int _ { 2 } ^ { 3 } \{ | \mathrm { x } - 2 | + [ \mathrm { x } ] \} \mathrm { dx }$

=$\int _ { 2 } ^ { 3 } ( x - 2 + 2 ) d x$

= + + 3x – +

= – $\left( 2 - \frac { 1 } { 2 } \right)$ + (6 – 2) –$\left( 3 - \frac { 1 } { 2 } \right)$ + – 2 = 7.