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Question

Question: <img src="https://cdn.pureessence.tech/canvas_37.png?top_left_x=1197&top_left_y=900&width=300&height...

dx =

A

e100−1e−1\frac { \mathrm { e } ^ { 100 } - 1 } { \mathrm { e } - 1 }

B

e−1100\frac { e - 1 } { 100 }

C

100 (e – 1)

D

e100−1100\frac { \mathrm { e } ^ { 100 } - 1 } { 100 }

Answer

100 (e – 1)

Explanation

Solution

x – [x]’s Period = 1

∑n=1100∫n−1nex−[x]dx=100∫01ex−[x]dx\sum _ { n = 1 } ^ { 100 } \int _ { n - 1 } ^ { n } e ^ { x - [ x ] } d x = 100 \int _ { 0 } ^ { 1 } e ^ { x - [ x ] } d x

= 100