Area of bounded region using riemann sums f(x) = x^2 g(x) = x+6 255. Determine the...
Estimate the area of the region bounded by the graph of f(x)-x + 2 and the x-axis on [0,4] in the following ways a. Divide [0,4] into n = 4 subintervals and approximate the area of the region using a left Riemann sum. Illustrate the solution geometrically. b. Divide [0,4] into n = 4 subintervals and approximate the area of the region using a midpoint Riemann sum· illustrate the solution geometrically. C. Divide [04] into n = 4 subintervals and...
6. [10 pts] The table below gives the values of a function f(x, y) on the square region R-[0,4] x [0,4]. -2-4-3 You have to approximate f(r, y) dA using double Riemann sums. Riemann sum given (a) What is the smallest AA ArAy you can use for a double the table above? (b) Sketch R showing the subdivisions you found in part (a). (e) Give upper and lower estimates of y) dA using double Riemann sums with subdivisions you found...
. 110 pts] Th R -[0,4] x [0,4] e table below gives the values of a function f(x,) on the square region 234 2 42 24-3 You have to approximate |f(x, y) dA using double Riemann sums (a) What is the smallest AA- ArAy you can use for a double Riemann sum given the table above? (b) Sketch R showing the subdivisions you found in part (a) (c) Give upper and lower estimates of f(x, y) dA using double Riemann...
4. Riemann sums - ten rectangles same area A) with ten rectangles in Repeat problem 3 (same function f(x) = place of five: a) Draw ten rectangles to visualize a Riemann sum of your choice for the area A. b) Give an estimate of the area A using the Riemann sum (the sum of the areas of the ten rectangles). 3. Riemann sums-five rectangles a) Sketch the graph of the function f(x) = b) Sketch the area A bounded by...
Notesheet 5.1-Areas and Distances(Riemann Sums) Book Section 5.1: NAME: 1. Fill in the blanks to make mathematically correct sentences. A Riemann Sums is a of estimating the under a by dividing the into b. The Right Riemann sum formula for the area under flu) on (a, b) is given by: c. The Left Riemann sum formula for the area under f(x) on (a,b] is given by: c. The Midpoint Riemann sum formula for the area under f(x) on (0,5) is...
5. (12 pts.) Consider the region bounded by f(x) 4-2x and the x-axis on interval [-1, 4] Follow the steps to state the right Riemann Sum of the function f with n equal-length subintervals on [-, 4] (5 pts.) a. Xk= f(xa) (Substitute x into f and simplify.) Complete the right Riemann Sum (do not evaluate or simplify): -2 b. (1 pt.) lim R calculates NET AREA or TOTAL AREA. (Circle your choice.) Using the graph, shade the region bounded...
11. (7pts) Set up an expression for | 2*3z* dr as a limit of sums. (That is, set up the infinite Riemann sum.) You do not have to evaluate the sum! 12. (10pts)Find the area between the curves f(x) = -2x and g(x) = x2 + 7x + 6. 13. (10pts) Find the volume of the solid obtained by rotating the region bounded by y = Væ+3, x = 4, and y = 0 about the x-axis.
5. The Area of a Plane Region. (15 points) a. Find the left Riemann sum for the region bounded by the graph of f(x) = x2 + 2x + 3 and the x-axis between x = 0 and x = 2. (Limit Definition) b. Use Fundamental Theorem of Calculus to solve part a. n с = пс Ži=n(n+1) n(n + 1)(2n +1) 6 =1 i=1 O, O A &
6. (6 pts) (x)-4-2x on [0,4] a. b. Sketch the function on the given interval. Approximate the net area bounded by the graph of f and the x-axis on the interval using a left, right, and midpoint Riemann sum with n-4 c. Use the sketch in part (a) to show which intervals of [a,b] make positive and negative contributions to the net area. (4 pts Use geometry (not Riemann sums) to evaluate the following definite integrals Sketch a graph of...
estimate the area between y=e^-x^2/4 and the x-axis on -2,1 using Riemann sums with the indicated number of rectangles a. 4 rectangles b.8 rectangles