Problem 1E: Let I=04f(x)dx, where f is the function whose graph is shown. (a) Use the graph to find L2, R2, and... Problem 2E: The left, right, Trapezoidal, and Midpoint Rule approximations were used to estimate 02f(x)dx, where... Problem 3E: Estimate 01cos(x2)dx using (a) the Trapezoidal Rule and (b) the Midpoint Rule, each with n = 4. From... Problem 4E: Draw the graph of f(x)=sin(12x2) in the viewing rectangle [0, 1] by [0, 0.5] and let I=01f(x)dx. (a)... Problem 5E: Use (a) the Midpoint Rule and (b) Simpsons Rule to approximate the given integral with the specified... Problem 6E: Use (a) the Midpoint Rule and (b) Simpsons Rule to approximate the given integral with the specified... Problem 7E: Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpsons Rule to approximate the given... Problem 8E: Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpsons Rule to approximate the given... Problem 9E: Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpsons Rule to approximate the given... Problem 10E: Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpsons Rule to approximate the given... Problem 11E: Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpsons Rule to approximate the given... Problem 12E: Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpsons Rule to approximate the given... Problem 13E: Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpsons Rule to approximate the given... Problem 14E: Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpsons Rule to approximate the given... Problem 15E: Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpsons Rule to approximate the given... Problem 16E: Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpsons Rule to approximate the given... Problem 17E: Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpsons Rule to approximate the given... Problem 18E: Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpsons Rule to approximate the given... Problem 19E: (a) Find the approximations T8 and M8 for the integral 01cos(x2)dx. (b) Estimate the errors in the... Problem 20E: (a) Find the approximations T10 and M10 for 12e1/xdx. (b) Estimate the errors in the approximations... Problem 21E: (a) Find the approximations T10, M10, and S10 for 0sinxdx and the corresponding errors ET, EM, and... Problem 22E: How large should n be to guarantee that the Simpsons Rule approximation to 01ex2dx is accurate to... Problem 27E: Find the approximations Tn, Mn, and Sn. for n = 6 and 12. Then compute the corresponding errors ET,... Problem 28E: Find the approximations Tn, Mn, and Sn. for n = 6 and 12. Then compute the corresponding errors ET,... Problem 29E: Estimate the area under the graph in the figure by using (a) the Trapezoidal Rule, (b) the Midpoint... Problem 30E: The widths (in meters) of a kidney-shaped swimming pool were measured at 2-meter intervals as... Problem 31E: (a) Use the Midpoint Rule and the given data to estimate the value of the integral 15f(x)dx. (b) If... Problem 32E: (a) A table of values of a function g is given. Use Simpsons Rule to estimate 01.6g(x)dx. (b) If 5 ... Problem 33E: A graph of the temperature in Boston on August 11, 2013, is shown. Use Simpsons Rule with n = 12 to... Problem 34E: A radar gun was used to record the speed of a runner during the first 5 seconds of a race (see the... Problem 35E: The graph of the acceleration a(t) of a car measured in ft/s2 is shown. Use Simpsons Rule to... Problem 36E: Water leaked from a tank at a rate of r(t) liters per hour, where the graph of r is as shown. Use... Problem 37E: The table (supplied by San Diego Gas and Electric) gives the power consumption P in megawatts in San... Problem 38E: Shown is the graph of traffic on an Internet service providers T1 data line from midnight to 8:00... Problem 39E: Use Simpsons Rule with n = 8 to estimate the volume of the solid obtained by rotating the region... Problem 40E Problem 41E Problem 42E: The figure shows a pendulum with length L that makes a maximum angle 0 with the vertical. Using... Problem 43E: The intensity of light with wavelength traveling through a diffraction grating with N slits at an... Problem 44E: Use the Trapezoidal Rule with n = 10 to approximate 020cos(x)dx. Compare your result to the actual... Problem 45E Problem 46E: Sketch the graph of a continuous function on [0, 2] for which the right endpoint approximation with... Problem 47E Problem 48E: Show that if f is a polynomial of degree 3 or lower, then Simpsons Rule gives the exact value of... Problem 49E: Show that 12(Tn+Mn)=T2n. Problem 50E format_list_bulleted