26 sin(x) dx. (Round your answers to six decimal places.) Jo (a) Find the approximations T. 10 M10 and S,0 for T10 = 51.571612 M10 52 214458 %3D S10 = 52.002847 Find the corresponding errors E, E, and Es. (Round your answers to six decimal places.) = 0.428388 ET EM -0.214458 %3D Es -0.002847 %3D (b) Compare the actual errors in part (a) with the error estimates found by using the smallest possible values for K in the theorem about error bounds for trapezoidal and midpoint rules and the theorem about error bound for Simpson's rule. (Round your answers to six decimal places.) IEI S 0 671802 IE s 0.335901 IE s 0.004420 (c) Using the values of K from part (b), how large do we have to choose n so that the approximations T M and S to the integral in part (a) are accurate to within 0.00001? For Tn=1988 For n1406 M For Sn=41 x x x

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