Use Simpson's Composite rule with n = 4, 6, 8. . . until successive approximations to the following integrals agree to within 10ˆ’6. Determine the number of nodes required. Use the Adaptive Quadrature Algorithm to approximate the integral to within 10ˆ’6, and count the number of nodes. Did Adaptive quadrature produce any improvement?

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x cosx dx x sin dx x" cosx dx sin x dx