Approximation using inscribed rectangles.

[mattflint50]

heres the problem:

Let the integral from 0 to x of [cos(t/2) + (3/2)] dt on the closed interval [0, 4pi]

it asks us to approximate f(2pi) using the inscribed rectangle method, find f'(2pi) and find the average valuse of f'(x) on the interval [0,4pi].

Our teacher hasn't taught us how to use inscribed rectangles and this question is bonus if we figure it out.

 

[pka]

Our teacher hasn't taught us how to use inscribed rectangles and this question is bonus if WE figure it out.

Because it is extra credit, I do think you need to do it yourself.

Some hints.
Graph the function g(t)=cos(t/2)+(3/2)?
Is it decreasing from 0 to 2pi ?
Lookup right and left hand sums.
Which ones are inscribed and when?