Find the approximations T_10, M_10, and S_10 for the integral integral^2_0 xe^x

Question

Find the approximations T_10, M_10, and S_10 for the integral integral^2_0 xe^x dx. Find the approximations T_8, M_8, and S_8 for the integral integral^pi_0 sin(x^2)dx. Estimate the errors E_M, E_T, and E_S in the approximation of the integral integral^4_1 squareroot x dx with how large do we have to choose n so that the approximations T_n, M_n, and S_n to the integral within 10^-4? how large do we have to choose n so that the approximations T_n, M_n to the integral integral^2_0 tan to within 10^-4? integrate: integral tan^-1(x)/1 + x^2 dx

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