7-18 Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpson's Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) 7. Vx3 – 1 dx, n 1 Ux, Vr3 =10 + r6
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- Use (a) the Trapezoidal Rule, (b) the Midpoint Rule,and (c) Simpson’s Rule n=10 with to approximate the givenintegral. Round your answers to six decimal places. ∫24 1/In x dxSolve the line integral provided in the attatched image. (C is the curve in the xy plane that is given by the equation x4 - 6xy2 = 4y2, from the point at the origin (0,0) to the point (2,1))Use (a) the Trapezoidal Rule integral 1to 4 cos 2 x dx with n= 8
- Consider a χ2-curve with df = 16. Obtain the χ2-value that has area a. 0.025 to its left. b. 0.975 to its left.Estimate the error in using the Trapezoidal Rule with n=8 when approximating the inetegral of (6x+3)dx with an upper bound of 6 and lower bound of 4. Which answer is correct? a. 0.0051 b. 0.0000 c. 0.0204 d. 0.0251Determine the value of ∫0.1 3.1 x cosx dx by using N = 4 of the trapezoidal rule. Round-off to three decimal places. NOTE: LL = 0.1, UL = 3.1.
- Solve using excell. Determine the approximate integration of the following using simple & modified trapezoidal, 1/3 Simpson's and 3/8 Simpson's Rule. ⌠31 (e0.5x + sin2x) dx. use n=4 ⌠41 cosx(0.25x2 + 1.90)dx, use n=3Derive the Simpson rule with f(x) = ax^2 + bx + c going through points xi−1, xi, and xi+1. Determine a, b, and c from the three equations given at the three data points first and then carry out the integration over the two slices with the quadratic curve being the integrand.Why would it not be 2e^xsiny? You end with two of them if you have "integral" dx + "integral" dy = C
- How can I evaluate ∭x2 dV, where E lies between the spheres ρ = 1 and ρ = 3 and above the cone Φ = π/4? Any help would be greatly appreciated :)Find the solution u(ρ, φ) of Laplace’s equaiton in the cylinder 0 ≤ ρ < R satisfying the boundaryconditions u(R, φ) = 1 + cos 2φ + 3 sin 3φ, −π ≤ φ ≤ π.Given the final result as I = 4 a) Trapezoid method and b) 1/3 Simpson method Calculate it with its integral, find its absolute errors.