Expectation value of kinetic energy

[White_M]

Homework Statement

Given the following hypothetic wave function for a particle confined in a region -4≤X≤6:

ψ(x)= A(4+x) for -4≤x≤1
A(6-x) for 1≤x≤6
0 otherwise


Using the normalized wave function, calculate the expectation value of the kinetic energy.

Homework Equations

I used ∫ψ*ψdx=1 to normaize the function and got that |A|^2=3/250.

The Attempt at a Solution

I know that T=\frac{\hat{P^2}}{2m}=\frac{-h^2}{2m}\frac{d^2}{dx^2}
I tried to calculate it using <T>=∫ψ*Tψ using the expression above and got zero which is not correct.

The solution given by the book is <T>=-\frac{h^2}{2m}\frac{3}{250}(0*1-5*2+0*1)=\frac{3h^2}{50m}

p.s
h in the formulas above is \frac{h}{2pi}

What am I doing wrong?

Thanks. Y.

 

[clamtrox]

The second derivative is not zero everywhere.