Answer:
Step-by-step explanation:
(1). A = π r²
A = 4 π
Area of shaded region is
=
or
(2). C = 4 π
In this case, the length of the bigger arc and the area of shaded region happen to be the same.
The length of the arc ADB is
or
B-y is the another factor
9.88,10.19,11.15,11.70,12.01,12.46,13.22,13.29,14.00,14.38,14.50,14.50,15.14,15.16,15.16,15.16,15.54,15.96,16.20,16.22,16.44,17.
Arada [10]
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Answer:
See below
Step-by-step explanation:
We start by dividing the interval [0,4] into n sub-intervals of length 4/n
![[0,\displaystyle\frac{4}{n}],[\displaystyle\frac{4}{n},\displaystyle\frac{2*4}{n}],[\displaystyle\frac{2*4}{n},\displaystyle\frac{3*4}{n}],...,[\displaystyle\frac{(n-1)*4}{n},4]](https://tex.z-dn.net/?f=%5B0%2C%5Cdisplaystyle%5Cfrac%7B4%7D%7Bn%7D%5D%2C%5B%5Cdisplaystyle%5Cfrac%7B4%7D%7Bn%7D%2C%5Cdisplaystyle%5Cfrac%7B2%2A4%7D%7Bn%7D%5D%2C%5B%5Cdisplaystyle%5Cfrac%7B2%2A4%7D%7Bn%7D%2C%5Cdisplaystyle%5Cfrac%7B3%2A4%7D%7Bn%7D%5D%2C...%2C%5B%5Cdisplaystyle%5Cfrac%7B%28n-1%29%2A4%7D%7Bn%7D%2C4%5D)
Since f is increasing in the interval [0,4], the upper sum is obtained by evaluating f at the right end of each sub-interval multiplied by 4/n.
Geometrically, these are the areas of the rectangles whose height is f evaluated at the right end of the interval and base 4/n (see picture)

but

so the upper sum equals

When
both
and
tend to zero and the upper sum tends to
