Integral from 0 to 1 of sqrt(1+x^2) n M_n T_n S_n 2 1.140388203202208 1.162570384968221 1.147724919562112 4 1.145949638700229 1.151479294085214 1.147782263790879 8 1.147333061452948 1.148714466392722 1.147792857161891 16 1.147678475868991 1.148023763922835 1.147793529766206 32 1.147764801833114 1.147851119895913 1.147793571886939 64 1.147786381595758 1.147807960864513 1.147793574520714 128 1.147791776428382 1.147797171230136 1.147793574685343 256 1.147793125129785 1.147794473829259 1.147793574695633 512 1.147793462304713 1.147793799479521 1.147793574696276 1024 1.147793546598418 1.147793630892118 1.147793574696316 Integral from 0 to 2 of ln(1+e^x) n M_n T_n S_n 2 2.675490262162859 2.723299283319682 2.691040647225270 4 2.687481828888602 2.699394772741271 2.691426602548467 8 2.690462509894951 2.693438300814936 2.691452810172825 16 2.691206610218078 2.691950405354944 2.691454440201614 32 2.691392568535775 2.691578507786511 2.691454541930367 64 2.691439053944244 2.691485538161142 2.691454548286019 128 2.691450675035705 2.691462296052693 2.691454548683211 256 2.691453580292281 2.691456485544201 2.691454548708034 512 2.691454306605404 2.691455032918240 2.691454548709588 1024 2.691454488183624 2.691454669761827 2.691454548709681 Integral from 0 to pi of sqrt(x)*sin(x) n M_n T_n S_n 2 2.689295910694110 1.968701243215302 2.624934990953736 4 2.491013606568397 2.328998576954706 2.449097688201174 8 2.448367685409170 2.410006091761551 2.437008596697166 16 2.438453740267024 2.429186888585360 2.435580487526630 32 2.436082961332208 2.433820314426193 2.435364789706469 64 2.435507925940271 2.434951637879199 2.435328745696870 128 2.435367207894137 2.435229781909737 2.435322496586580 256 2.435332561085742 2.435298494901935 2.435321399232670 512 2.435323993260156 2.435315527993841 2.435321205691140 1024 2.435321867881042 2.435319760626997 2.435321171504719 Integral from 0 to 1 of 4/(1+x^2) n M_n T_n S_n 2 3.162352941176470 3.100000000000000 3.133333333333333 4 3.146800518393943 3.131176470588235 3.141568627450980 8 3.142894729591689 3.138988494491089 3.141592502458707 16 3.141918174308560 3.140941612041389 3.141592651224823 32 3.141674033796337 3.141429893174975 3.141592653552836 64 3.141612998641847 3.141551963485654 3.141592653589215 128 3.141597739852815 3.141582481063752 3.141592653589785 256 3.141593925155547 3.141590110458282 3.141592653589794 512 3.141592971481231 3.141592017806921 3.141592653589787 1024 3.141592733062653 3.141592494644072 3.141592653589790