(10) Using the method of partial fractions (and not some other method), evaluate 12 + 3x-1 x(x2 + 1) (4pts] Be sure to give your final answer in terms of the original variableMAT 1320B Final Exam 11 (12) We wish to find a numerical approximation (not the exact value!) for the integral using the midpoint rule. (a) Give the expression for this integral using a midpoint rule with n = 4. Write this expression as a sum that is ready to be evaluated, but do not evaluate it (that is, use all provided information but do not simplify the expression). 2 x* dx (b) Determine the smallest value of n that will guarantee that the approximation error using the midpoint rule for the integral / x4 dx is at most 0.01. Write a bound for this smallest n that is ready to be evaluated, but do not need to evaluate it.MAT 1320B Final Exam [Apts)(11) We wish to evaluate J Van de. = 10 show that (a) By choosing an appropriate trigonometric substitution and simplifying the result, 2 4 do = / tan'(0) sec(0 ) do . (b) Evaluate / tan' (0) sec(0) do in terms of 0. (c) Express your answer to part (b) in terms of x according to the trigonometric substi tution you applied in part (a). Your final answer may not include any trigonometri functions or inverse trigonometric functions