Calculus question. complete and explain the following.

We're approximating the area under the graph of the function over the interval [-2, 2] by

Splitting [-2, 2] into 4 intervals gives

[-2, -1], [-1, 0], [0, 1], [1, 2]

Each subinterval has length 1. The right endpoints of the -th subinterval, where , are given by the (arithmetic) sequence

The area of the rectangle over the -th subinterval is

and so the definite integral is approximately

There are well-known formulas for computing the sums of powers of consecutive (positive) integers. The ones we care about are

So we get

d 25 pi/6

step-by-step explanation:

the diameter is 10 inches

the radius is 1/2 of the diameter or 5 inches

the area of the circle is

a = pi r^2

  = pi 5^2

  = 25 pi

the slice is 60 degrees of the entire circle.

60 degrees out of 360   60/360 = 1/6

the area of the slice is 1/6 of the circle

a slice = 1/6 a circle

a slice = 1/6 * 25 pi