HW Approximations/Charts (Trapezoidal Rule/Riemann Sums) Name: 2003 (Calculator) 2)The rate of fuel consumption, in gallons per minute, recorded during an airplane flight is given by a twice differentiable and strictly increasing function R of time t. The graph of R and a table of selected values of R(t) for the time interval
Numerical approximations to definite integrals Use of Riemann sums (using left, right and midpoint evaluation points) and trapezoidal sums to approximate definite integrals of functions represented algebraically, graphically, and by table of values.
Integral Approximation Calculator. Use this tool to find the approximate area from a curve to the x axis. Read Integral Approximations to learn more. Note: use your eyes and common sense when using this! Some curves don't work well, for example tan(x), 1/x near 0, and functions with sharp changes give bad results. Plus and Minus
b. [3 points] Write out the terms of a left Riemann sum with 3 equal subdivisions to estimate the integral from (a). Does this sum give an overestimate or an underestimate of the integral? Solution: This left Riemann sum is 2·5+2·6+2·11 = 44. Since M(t) is increasing on the interavel [0,6], this is an underestimate of the integral from (a).
Final integral value is the sum of integral for each partial intervals. To evaluate a new integration methods based on eqally spaced intervals you may use the following calculator having an input box for entering weights:
shown in the table below. t (minutes) v(5) (miles per minute) 30 40 20 25 35 10 15 7 4.5 2.4 2.4 4.3 7.3 9.2 9.5 a) Use a midpoint Riemann sum with four subintervals of equal length and values from the table to approximate Show the computations that lead to your answer. Using correct units, explain the meaning of in terms of the plane's flight.