Originally Posted by

**Archie Meade**

Now, the graph alternates from positive to negative, so be careful with your limits,

to avoid getting a result of zero, or subtracting any part of the area.

You are correct to look for the integral of the modulus.

However, you need to locate the x-axis crossing points of your graph

in order to evaluate the area between the resulting function and the x-axis

and if it is symmetrical.

$\displaystyle u=sint,\ du=costdt$

$\displaystyle t=0,\ u=0$

$\displaystyle t=\frac{{\pi}}{2},\ u=1$

**What does this notation mean?**

$\displaystyle \displaystyle\huge\ (4)3a\int_{0}^1u\ du$

gives the area between the curve and the x-axis.

You may also express

$\displaystyle costsint=\frac{1}{2}sin2t$