# Question:Simplifying expressions(symbolic integration)

## Question:Simplifying expressions(symbolic integration)

Maple 13

Hi all,

I have the following functions.

`restart:with(IntegrationTools):N:=4:i:='i':for i from 1 to N do    assume(x[i-1]::constant):    assume(x[i+1]::constant):    assume(x[i-1]::constant):    assume(h::constant):`
` phi[i](t):=piecewise(t>=x[i-1] and x[i]>t, (t-x[i])/(h), x[i]`
`(x[i+1]-t)/(h), 0);`
`end do;`
`## my goal is solve the integrals involving phi[i]'s as integrand and x[i]'s as its limits.`
`## as a test case I tried to calculate Int( diff( phi[1], t)* diff( phi[1], t), t=x[0]..x[2]);`
` `
`V:=Int(diff(phi[1](t), t)*diff(phi[1](t), t), t=x[0]..x[2]);`
`addionally assuming(x[0]<x[1] and x[1]<x[2]`
` and x[2]<x[3]);`
`Parts(V, phi[1]);`
` `
`## The output pretty much looks what we get by hand, but there are plently`
` of Heaviside functions involve. `
`By a simple look at the output those Heaviside functions have to`
` disappear by using the order x[0]>x[1]>x[2].`
`But it isnt. `
`Would any body please point out my mistake or give me some better idea?`
` `
`Thanks!!!`
` `
` `
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