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: The second choice is correct: slope is 3/4, y-intercept is 1
Step-by-step explanation: The y-intercept is where the line crosses the y-axis.
Look for places where the line intersects the grid at "cross-points" like (-4,-2) (0,1) and (4,4)
The slope is rise/run.
The difference in y-values is the rise. 4-1=3 1-(-2) is 3.
The rise is 3.
The difference in x-values is the run. 4-0=4 0-(-4) = 4
The run is 4
Rise/run = 3/4 That is the slope.
It would be 9 because 2x9=18. Then 18+-2=16.
Answer:
Step-by-step explanation:
Correct me is I'm wrong but I believe its a independent variable.
