For the function given below, find a formula for the riemann sum obtained by dividing the interval [a, b] into n equal subintervals and using the right-hand endpoint for each c subscript k. then take a limit of this sum as n right arrow infinity to calculate the area under the curve over [a, b]. f(x)equals2x over the interval [2,4].

We split [2, 4] into subintervals of length ,

so that the right endpoints are given by the sequence

for . Then the Riemann sum approximating

is

The integral is given exactly as , for which we get

To check: we have

80π/3 or about 83.775

step-by-step explanation:

since a cone is 1/3 of a cylinder, we need to find the base's area. since area = πr^2, we get 16π. then, multiplying this by 5, we get 80π. dividing by 3, since the cone's volume is 1/3 of that of a cylinder's, we get 80π/3.

hope this !

ghjmutmum

step-by-step explanation: