Question: 5. Let f(x) = 1 + x2 and consider f(x) dx. (a) Evaluate [f(x) da. (b) Find the Taylor series of f(x). Replace f(x) by

5. Let f(x) = 1 + x2 and consider f(x) dx.

5. Let f(x) = 1 + x2 and consider f(x) dx. (a) Evaluate [f(x) da. (b) Find the Taylor series of f(x). Replace f(x) by its 4th order Taylor polynomial to approximate f(x) da . Compute error by comparing with the correct value. (c) Interpolate f(x) at n = 7 evenly-spaced points in [-1, 1]. Replace f(x) by the interpolating polynomial to approximate / f(x) dx . Compute error by comparing with the correct value

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