Split up the interval [0, 2] into <em>n</em> equally spaced subintervals:
![\left[0,\dfrac2n\right],\left[\dfrac2n,\dfrac4n\right],\left[\dfrac4n,\dfrac6n\right],\ldots,\left[\dfrac{2(n-1)}n,2\right]](https://tex.z-dn.net/?f=%5Cleft%5B0%2C%5Cdfrac2n%5Cright%5D%2C%5Cleft%5B%5Cdfrac2n%2C%5Cdfrac4n%5Cright%5D%2C%5Cleft%5B%5Cdfrac4n%2C%5Cdfrac6n%5Cright%5D%2C%5Cldots%2C%5Cleft%5B%5Cdfrac%7B2%28n-1%29%7Dn%2C2%5Cright%5D)
Let's use the right endpoints as our sampling points; they are given by the arithmetic sequence,
where 
. Each interval has length 
.
At these sampling points, the function takes on values of
We approximate the integral with the Riemann sum:
Recall that
so that the sum reduces to
Take the limit as <em>n</em> approaches infinity, and the Riemann sum converges to the value of the integral:
Just to check:
Answer:
9 pitchers
Step-by-step explanation:
Given
Cylinder 1:
Cylinder 2:
Required
How many pitchers' cylinder 2 can fill
First, we calculate the volume of both cylinders
Volume is calculated as:
For A:
For B:
In (a):
So, we have ve:
<em>If the first cylinder can fill 1, then the second can fill 9 pitchers</em>
I DONT KNOW JUST STRAT WITH THE BEGGINIG OF THE SENTENCE
sin(x) = opp/hyp
cos(x) = adj/hyp
tan(x) = opp/adj
sin(x) = 3.9/8.1
sin(x) = 0.481
Inverse sin of 0.481 = 28.8 degrees
Each answer should be between 0 and 90 :)
