(b) (10%) The integral in (a) can be approximated by integrating the linear approximation of the integrand, i.e. let $$f(x) = \frac{1 + x}{\sqrt{1 - x^2}} \approx f(0) + f'(0) x$$ Approximate $\int_{-1}^0 f(x) \, dx$ by evaluating $$\int_{-1}^0 (f(0) + f'(0) x) \, dx$$

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