I have to calculate the area of the shaded graph (in the link). Seeming as no equations are given, how do I calculate it?
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It's hard to read the graph but it's just 0.1π, 0.2π... 2.0π.
I have to calculate the area of the shaded graph (in the link). Seeming as no equations are given, how do I calculate it?
Untitled | Flickr - Photo Sharing!
It's hard to read the graph but it's just 0.1π, 0.2π... 2.0π.
To me it seems like it is a sine and cosine graph.
You would need to develop an equation to be able to calculate the area accurately:
$\displaystyle y = a*sin(bx)$
$\displaystyle y = a * cos(bx)$
Where a and b are constant values.
To me it seems its maximum is 4.5 and minimum is -4.5. Thus constant a must be 4.5.
One full cycle seems to be 2.0π. If you are working in radians, constant b must be $\displaystyle 2\pi$/2. If working in degrees, b = 360/2.
$\displaystyle y = 4.5*sin(\pi {x})$
$\displaystyle y = 4.5 * cos(\pi {x})$
(For working in radians)
There once you have your 2 equations, you can integrate between 0 and 2 to find the area.
Oh sorry I misinterpereted the figures on your graph.
Now I take a closer look, 2.0π actually meant $\displaystyle 2\pi$. I thought π was the units...
Forget what I said about b being a constant. It stretches out like a normal graph - from 0 to $\displaystyle 2\pi$.
Thus:
$\displaystyle y = 4.5*sin(x)$
$\displaystyle y = 4.5 * cos (x)$
To make finding the area of the shaded part easier, move the graph up by 4.5 so that no part of it is in the negative part, below the x-axis.
$\displaystyle y = 4.5*sin(x)+4.5$
$\displaystyle y = 4.5 * cos (x)+4.5$
To find the area:
Integrate between 0 to $\displaystyle \frac{1}{4}\pi$, and do the cosine graph subtracted the sine graph.
Then integrate between $\displaystyle \frac{1}{4}\pi$ to $\displaystyle \frac{5}{4}\pi$, and do the sine graph subtracted the cosine graph this time.
Finally integrate between $\displaystyle \frac{5}{4}\pi$ to $\displaystyle \frac{8}{4}\pi$, and do the cosine graph subtracted the sine graph.
Add all of these together and you will find your shaded area.