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IntegrationTools[Split] - split the range of integration

Calling Sequence

Split(v, c)

Parameters

v

-

definite or indefinite integral

c

-

splitting point(s)

Description

• 

The Split command splits the range of integration of v: acfxⅆx+cbfxⅆx=abfxⅆx.

• 

The second parameter c is a splitting point or a list of splitting points. Alternatively, a list of the form [f(i), i = m..n] can be specified. In this case [seq(f(i), i=m..n)] will be used as the splitting points if m and n are constants.  If at least one of m or n is symbolic, the points f(m), f(m+1), ... , f(n-1), f(n) will be used and the result is correct as long as (m-n) is an integer.

Examples

withIntegrationTools:

V:=∫12πn1sinxⅆx

V:=∫12πn1sinxⅆx

(1)

SplitV,2π

∫12πsinxⅆx+∫2π2πn1sinxⅆx

(2)

SplitV,2π,4π,6π

∫12πsinxⅆx+∫2π4πsinxⅆx+∫4π6πsinxⅆx+∫6π2πn1sinxⅆx

(3)

SplitV,2πi,i=1..n1

∫12πsinxⅆx+_j=1n2∫2π_j2π_j+1sinxⅆx+∫2πn12πn1sinxⅆx

(4)

See Also

IntegrationTools


Download Help Document

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