Question

calculate the right riemann sum with 8 subintervals on f(x)=10-x on the interval (3,5)

Answer 1

47/4 or 11.75

Answer 2

please tell me how you got that?

Answer 3

Sure. The interval is 2 / 8 = 0.25.

Then, since it's a right Riemann sum, the x-values you're going to want to calculate are (10 - 3.25 = 6.75), (10 - 3.5 = 6.5), (10 - 3.25 = 6.25), and so forth with a step of 0.25 every time.

Then you multiply 0.25, the width of the interval, by (6.75, 6.5, 6.25...5.25, 5), which is the set of heights you calculated. The answer to that is 11.75.

Answer 4

how do you get 3.25 ? and 3.5? and 3.25?

Answer 5

i have another one also the right riemann sum in 6 sub intervals for f(x)=2x^2-5x+9

Answer 6

So you know the step is 0.25, since the interval is (3, 5) and you want 8 subintervals. 5 – 3 = 2, and 2 / 8 = 0.25. Then since it’s a right Riemann sum, you want the right value of each rectangle. The x-values you’re going to consider are 3 + 0.25 = 3.25, 3.25 + 0.25 = 3.5, 3.5 + 0.25 = 3.75, and so on. The equation is 10 – x, so you plug the x-values in to get the y-value, which is the height of the rectangle. You multiply that with the width of each subinterval, 0.25, and sum up the area of all the rectangles to get the Riemann sum.

Answer 7

ok so how do i break this one down the right riemann sum in 6 sub intervals for f(x)=2x^2-5x+9?

Answer 8

What's the main interval?

Answer 9

1,4

Answer 10

Okay. so 4 - 1 = 3, and you want 6 sub intervals, so the step is going to be 3 / 6 = 0.5. Starting from 1, you do 1 + 0.5 = 1.5, 1.5 + 0.5 = 2, 2 + 0.5 = 2.5, and so on to get a set of x-values (1.5, 2, 2.5, 3, 3.5, 4).

Then you plug those into the function to get the set of y-values, multiply that set by 0.5, the width of each interval, and sum up the areas to get your answer!

Answer 11

And just in case you wanted to verify, the answer is 8.25.

Answer 12

thanks