Question

For each function, compute the two indicated approximations to the net area under the curve. Write out each approximation symbolically using sigma notation, with index i, and then compute it (by hand or by using your TI-36XPro or other inferior technology; round to3 decimal places). b. Rh)-22sinover 112,18] using midpoints for n-8 and also for n- 80

Answer 1

Given that The two indicated approximations the net area under the curve. Assume: f (x) = 2x: a = 1, b = 2, n = 5 For the rectangle the interval from x = 1 to x = 2 derived into 5 of length angle x given by angle x = b - a/n = 2 - 1/5 = 002 Therefore the points on x - axis making the beginning f sub - intervals are x_1 = 1, x_2 = 1.2, x_3 = 1.4, x_4 = 1.6, x_5 = 1.8 the function at these points are given by f (x_1) = 2 f (x) x_2 = 2.4 f (x_3) = 2.8 f (x_4) = 3.2 f (x_5) = 3.6 \r\n the approximation of the area given by A = angle x [f (x_1) + f (x_2) + f (x_2) + f (x_4) + f (x_5)] (1) using complete data above eqn. A = 0.2 [2