Getting the angular velocity using the angular acceleration graph

[dahoom102]

Homework Statement

The graph below shows a plot of angular acceleration in rad/s2 from t=0 to t = 8s, the angular velocity at t=0 is 5rad/s ccw. the angular velocity at t=8 is

Relevant Equations

α=dω/dθ

The answer here is A
What i did is getting the area as follows,
2×4×1/2 +3×-6×1/2 +4×-6 = -29
and then use this
Δω=ωf-ωi
-29=ωf-5
ωf=24
but there is no such choice.

 

[BvU]

Why 4x-6 (in your language) ?

 

[dahoom102]

Why 4x-6 (in your language) ?

oh my mistake I didn't notice thanks a lot!

 

[kuruman]

Relevant Equations:: α=dω/dθ

$\alpha = \dfrac{d\omega}{dt}=\omega \dfrac{d\omega}{d \theta} .~~$