Find the value of "f" on the top "9" and in the botton "1" x^2dx using four rectangles of equal width, with each left end-point used to find the height of each rectangle.

a) 2(1+9+25+49)
b) 2(9+25+49+81)
c) 0.5(1+9+25+49)
d) 0.5(9+25+49+81)

please helppppp

You apparently want

∫[1,9] x^2 dx
using 4 rectangles of width 2, evaluating at the left sides.
You really need to study this some. Draw the graph and the rectangles; use various online Riemann Sum calculators, etc.
The 4 endpoints are obviously x=1,3,5,7. So, evaluate x^2 there to get the height of the rectangles.

Now, which of those sums seems likely to be the total area of the 4 rectangles?

To find the value of "f" on the top "9" and in the bottom "1" x^2 dx using four rectangles of equal width, we need to use the left end-points to find the height of each rectangle.

Let's break down the process step by step:

Step 1: Determine the width of each rectangle.
Since we are using four rectangles of equal width, we need to divide the interval [1,9] into four equal parts. The width of each rectangle, denoted as Δx, can be calculated by taking the difference between the upper and lower bounds of the interval and dividing by the number of rectangles.
Δx = (9 - 1) / 4 = 2

Step 2: Calculate the height of each rectangle using the left end-point.
Since we are using the left end-points, we need to evaluate the function x^2 at the x-values of the left end-points of each rectangle (1, 3, 5, and 7).

For the first rectangle:
x = 1
Rectangle 1 Height = f(1) = (1)^2 = 1

For the second rectangle:
x = 3
Rectangle 2 Height = f(3) = (3)^2 = 9

For the third rectangle:
x = 5
Rectangle 3 Height = f(5) = (5)^2 = 25

For the fourth rectangle:
x = 7
Rectangle 4 Height = f(7) = (7)^2 = 49

Step 3: Sum up the areas of the rectangles.
The value of "f" is equal to the integral of x^2 dx over the interval [1,9], which can be approximated by the sum of the areas of the rectangles.

To find the sum of the areas, we multiply the sum of the heights of the rectangles by the width of each rectangle and apply the given formula.

Using the provided options:
a) 2(1+9+25+49)
b) 2(9+25+49+81)
c) 0.5(1+9+25+49)
d) 0.5(9+25+49+81)

Using the calculated rectangle heights, we can compare the sum of the areas to find the correct option:

2(1+9+25+49) = 2(84) = 168
2(9+25+49+81) = 2(164) = 328
0.5(1+9+25+49) = 0.5(84) = 42
0.5(9+25+49+81) = 0.5(164) = 82

Comparing the options to the sum of the areas, we can see that the correct option is:
c) 0.5(1+9+25+49)

Therefore, the value of "f" on the top "9" and in the bottom "1" x^2 dx using four rectangles of equal width, with each left end-point used to find the height of each rectangle is:
f = 0.5(1+9+25+49)