- #1

chwala

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- Homework Statement
- find the definite integral of

##\int_0^5 -x^3+3x^2+6x-8\,dx##

- Relevant Equations
- integration

##\int_0^5 [-x^3+3x^2+6x-8\,]dx##

##\int_0^1 [-x^3+3x^2+6x-8\,]dx= |-\frac {17}{4}|##

##\int_1^4 [ -x^3+3x^2+6x-8\,]dx= 16##

##\int_4^5[-x^3+3x^2+6x-8\,]dx= |-\frac {49}{4}|##

Therefore, total area is ##|-\frac {17}{4}|+ 16+|-\frac {49}{4}|=32.5##

now where my problem is,... my colleague indicated the answer as ##36.75##

who is right, or where have i made a blunder?

##\int_0^1 [-x^3+3x^2+6x-8\,]dx= |-\frac {17}{4}|##

##\int_1^4 [ -x^3+3x^2+6x-8\,]dx= 16##

##\int_4^5[-x^3+3x^2+6x-8\,]dx= |-\frac {49}{4}|##

Therefore, total area is ##|-\frac {17}{4}|+ 16+|-\frac {49}{4}|=32.5##

now where my problem is,... my colleague indicated the answer as ##36.75##

who is right, or where have i made a blunder?

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