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Integral Calculus

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Joined:	26 Jan 2007
Post:	5

22 Feb 2007 00:29:23 IST

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integral involving greatest integer sin[x....]

None

_[0]

^{[pie ]} x sin[x^2-

] where[.] denotes the greatest integer function.

how to solve this integral as well as draw the graph of x sin[x^2-pie].

how to draw the graph of sin[x^2-pie].

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Comments (1)

Bipin Dubey

Forum Expert

Joined: 23 Jan 2007

Posts: 7942

24 Feb 2007 12:31:36 IST

Like 3 people liked this

[x²-

] = -4 0<=x<

(

-3)
= -3

(

-3)<=x<

(

-2)
= -2

(

-2)<=x<

(

-1)
= -1

(

-1)<=x<

= 0

<=x<

(

+1)
= 1

(

+1)<=x<

(

+2)
= 2

(

+2)<=x<

(

+3)
= 3

(

+3)<=x<

(

+4)
= 4

(

+4)<=x<

(

+5)
= 5

(

+5)<=x<

(

+6)
= 6

(

+6)<=x<

Hence integrating x.sin[x²-

] in the above intervals sin[x²-

] becomes constant and we are left to integrate x .

After simplifying the integral comes out to be

I = [(4-

)/2].sin4 + (sin5)/2 + [(

²-

-6)/2].sin6

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