# calculus(Lab)

posted by .

Well, first graph the graph of f(x)=-1/10x^2 + 3
2. We are going to approximate the area between f and the x-axis from x = 0 to x = 4 using rectangles (the method of Riemann sums). This is not the entire area in the first quadrant, just most of it. Draw four inscribed rectangles of width 1 on the interval [0, 4] on you graph above.

3. What are the heights of each of the four rectangles? What is the total area of the rectangles? This area, although not the same as the area beneath the curve is an approximation for that area called the lower sum

4. The actual area between f and the x-axis on the interval [0, 4] is 28/3 . Why is one area greater?

5. How could you get a better approximation for the area beneath the curve if you still used inscribed rectangles?

## Similar Questions

1. ### calculus

consider the function f(x)= x^2/4 -6 Rn is the Riemann sum where the sample points are chosen to be the right-hand endpoints of each sub-interval. Calculate Rn for f(x)= x^2/4 -6 on the interval [0,4] and write your answer as a function …
2. ### Calculus

Approximate the area under the graph of f(x)and above the x-axis using 4 rectangles: f(x)=x(x) +2 using 4 rectangles at intervals 0,5
3. ### math

Given f (x) = √(7 + x) + 4 . Use the rectangle method to approximate the area on the interval [0, 8] using 4 rectangles. (Assume the graph goes through the midpoint of each rectangle.)
4. ### Calculus

Use a graphing calculator to graph f(x)=x^4-6x^3+11x^2-6x. Then use upper sums to approximate the area of the region in the first quadrant bounded by f and the x-axis using four subintervals.
5. ### calculus

The graph of f'(x) is shown for 0=< x =<10. The areas of the regions between the graph of f' and the x-axis are 20, 6, and 4, respectively. I'm going to describe the graph of f' since I can't post pictures. The first section …
6. ### Calculus

Set up a Riemann sum to estimate the area under the graph of f(x) = 5x 2 + 2 between x = 0 and x = 1 using 3 subdivisions and left endpoints. Draw the graph and the 3 rectangles
7. ### Riemann Sums

Use the Riemann Sums corresponding to 5 inscribed rectangles of equal width to approximate the integral a= 1, b= 3, (1/x)dx this is all for definite integral i just know x1=1.4, x2=1.8, x3=2.2, x4=2.6, x5=3.0 how do i continue
8. ### Calculus-Approximate areas

Estimate the area under the graph of f(x)= x^2 + 3 x from x=1 to x=10 using the areas of 3 rectangles of equal width, with heights of the rectangles determined by the height of the curve at a) left endpoints: b) right endpoints:
9. ### Calculus

Consider the function x^2+x-4 Estimate the area between the graph and the x-axis between x=2 and x=4 using four rectangles and right end points.
10. ### Calculus

Use Riemann sums and limits to compute the area bounded by f(x) = 10x+9 and the x axis between x=10 to x =5 The area is = to

More Similar Questions