Question: Evaluate the definite integral (J=int_{0}^{1} frac{d x}{1+x^{2}}) using: (a) an exact analytic formula obtained from calculus; (b) approximate methods: (i) the trapezoidal rule ((n=4)); (ii)
Evaluate the definite integral \(J=\int_{0}^{1} \frac{d x}{1+x^{2}}\) using:
(a) an exact analytic formula obtained from calculus;
(b) approximate methods: (i) the trapezoidal rule \((n=4)\); (ii) Simpson's rule \((2 m=4)\); and (iii) the Gaussian integration formula \((n=4)\).
(c) Compute the error bounds for the trapezoidal rule in part (b).
(d) Compare the results obtained in parts (a) and (b).
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a Analytical Solution The integral is of a standard form and its antiderivative is known as the inverse tangent function arctanx So the integral J can ... View full answer
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