Evaluate the integral S 3012 2/3 de using the two-point Gaussian quadrature rule. 1+16z4
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- Set up an integral to find the area inside the ellipse . Show all steps to demonstrate the trig substitution method to integrate manually. (x-4)^2/16 + y^2/9 = 1a. Approximate the following integral using the Trapezoidal, Simpson’s andMidpoint rules b. Approximate the following integrals using Gaussian quadrature with n =2Verify Green's Theorem by setting up and evaluating both integrals∫c y2dx + x2dy = ∫∫R ((∂N/∂x) - (∂M/∂y)) ∂Afor the path C: square with vertices (0,0), (10,0), (10,10), (0,10). Please give a detailed answer, noting any steps or formulas use.
- Find the area of the part of the paraboloid x = y2 + z2 that lies inside the cylinder y2 + z2 = 17.7 9) Use (a) the Trapezoidal Rule and (b) the Midpoint Rule to approximate the given integral with the specified value of n.Evaluate the integral of (3x²+9y²)dxdy if the interior limits has an upper limit of y and a lower limit of 0, and whose outer limit has an upper limit of 2 and lower limit of 0. A. 10 B. 20 C. 30 D. 40