I need help solving this definite integral, from x = -2 to x=e: f(x)=x-e, if x0 and f(x)=e^(x+2), if x

Question

I need help solving this definite integral, from x = -2 to x=e: f(x)=x-e, if x>0 and f(x)=e^(x+2), if x<=0
Thanks !

turingtest · Answer

you need to split this up into two integrals
where are you having trouble?

anonymous · Answer

I got final answer being -2+e^(e+3). I tried to check it but it was wrong according to geogebra :S

turingtest · Answer

is that first function$f(x)=x-e$ or $f(x)=x^{-e}$ ?

anonymous · Answer

$$f(X)=x-e, if x>0 \ f(x)=e^{x+2}, if x\le 0$$

turingtest · Answer

so what did you put for the first integral?

anonymous · Answer

we split into integral fropm -2 to near 0 (x-e) and from 0 to e (e^(x+2))

turingtest · Answer

good, so$$\int_{-2}^0x-edx+\int_0^ee^{x+2}dx$$right?

anonymous · Answer

exactly

turingtest · Answer

$$\int_{-2}^0x-edx+\int_0^ee^{x+2}dx=\frac{x^2}2-ex|_{-2}^0+e^{x+2}|_0^e=2+2e+e^{e+2}-e^2$$

anonymous · Answer

I tried to check, it is not checking, doing the calculation in geogebra, or wolfram alpha