root mean square question..

calculate the RMS (root mean square) of this function.

http://i50.tinypic.com/2iuq80x.jpg

the period T=4

the formula is

$\displaystyle V_{rms}=\sqrt{\frac{1}{T}\int_{0}^{T}V_r^2dt}$

$\displaystyle V_{rms}=\frac{1}{4}4 \int_{0}^{T}(4t)^2 dt$

i get a latex error here the code is:

V_{rms}=\frac{1}{4}4\int_{0}^{T}(4t)^2dt}

$\displaystyle V_rms=\sqrt{s}=\sqrt{\frac{16}{3}}$

the solution says that they divide the graph into 4 triangles

and they sum their areas

but they dont use the integral?

why they say (4t)^2

from where the 4t comes from?

why they say that its the root of the area

why they dont divide by the period?