integrate 9

limits -2 to 2 integrate min { x - [x] , - x - [x] } dx
[] denotes greatest integer function

7 Answers

1
Anurag Khandelwal ·

Is the ans -2

1
ankit mahapatra ·

Tell me the method i will tell u the ans later.

1
Anurag Khandelwal ·

U draw the graph:
For -2<x<0,
min(x-[x],-x-[x])=x-[x]={x}
=>Area=1/2+1/2=1

For 0<x<2,
min(x-[x],-x-[x])=-x-[x]
=>Area=-1/2-5/2=-3

Total area=1-3=-2
(Hopefully)

1
ankit mahapatra ·

What about without the graph?

24
eureka123 ·

it would be difficult without graph.......[1]

24
eureka123 ·

visualisng is the main problem here.......[1]

39
Dr.House ·

anurag`s method is correct.

otherwise ankit u can even try splitting into much cmaller intervals and then easily get result. and comeon u would be knowing the basic int x and {x} graphs na.

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