Question

is equal to

• A. 1000 (e – 1)
• B.
• C.
• D. $\frac { 1 } { \mathrm { e } - 1 } \left( \mathrm { e } ^ { 1000 } - 1 \right)$

Answer 1

Answer: (A)

1000 (e – 1)

Answer 2

= $\int _ { 0 } ^ { 1 } e ^ { x - [ x ] } d x$ + $\int _ { 1 } ^ { 2 } \mathrm { e } ^ { \mathrm { x } - [ \mathrm { x } ] } \mathrm { dx }$ +.....+ $\int _ { 999 } ^ { 1000 } e ^ { x - [ x ] } d x$ = $1000 \int _ { 0 } ^ { 1 } e ^ { x - [ x ] } d x$

[Q x – [x] is periodic with period = 1]

= 1000 $\int _ { 0 } ^ { 1 } e ^ { \mathrm { x } } \mathrm { dx }$ = 1000 (e – 1)