Question

Here is a graph of the function y =r(t) =tan(cos(πt)+0.5)+2:

ibb.co/9qQjRvJ (Copy paste the link into browser, or type)

Estimate the total area under this curve on the interval [0, 12] with a Riemann sum using 36 equal subdivisions and circumscribed rectangles. Hint: Use symmetry to make this problem easier. You get area =

Answer 1

Jiskha does not allow cut and paste, just because your computer
allows it, (mine does too), on this page it does not work.

I also notice you might have meant:
ibb.com/9qQjRvJ

(I put in the extra m in .com), I ended up at some German website saying:
"Schade - diese Seite existiert leider nicht mehr"
Sorry, this page does not no longer exist.

I was able to graph your equation by entering it into
Desmos.com/calculator and from [0,12] you have 6 repeats of the same loop.
Obviously because of symmetry we could just use [0,1] then multiply
that answer by 12.
Do you want the area between the curve and the x-axis?

Looks like you just want us to do your work for you.

Answer 2

The url worked fine for me.
Since the interval [0,12] contains six symmetric copies of the curve, and you want 36 intervals, then the total area is 12 times the area under the curve in [0,1.5]
So all you need to do is use right-hand sums (why not left sums?) to get
A = 12 * 0.5 * (f(0.5)+f(1.0)+f(1.5))