0-6 3 Evaluate e dx by Simpson's th rule, taking n=6. 8
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- Is there a number x such that ln x=2 ? If so, whatis that number? Verify the result.Using the definition of integral12. x^2 dx as a limit of a sum of rectangles, compute integral12. x^2 dx. (Hint: You will likely need to use the facts that Sigmai=1n i^2= n(n+1)(2n+1)/6 and Sigmai=1n i= n(n+1)/2)Use Simpson’s Rule with n= 10 to approximate the integral 0 to 1 e x2 dx
- A) for beta less than 1 B) for beta great than or equal 1 C) for beta less than or equal 1 D) for beta great than 1 E) for beta less equal 0 Please explainon the definite integral (bounds 0 to 1) of the function cos(x^2), using the trapezoidal rule, how large should n be for the approximation to be within 0.0001How large should n be to guarantee that the Simpson's Rule approximation to 5(e^x^2) (bounds 1 and 0) is accurate to within 0.00001?
- Find the indefinite integral ∫ (e2x − e−2x) / (e2x + e−2x) dx1) Calculate the area (A) of the limit domain by the equation curve y=1/x, x=(n-1), x=(x+1) and the axis. n>1 2) By using the Simpson method, show that A= 1/3*((1/(n-1))+(4/n)+(1/(n+1))) We will divide the interval [(n-1),(n+1)] into 2 sub-intervals of equal length. 3) Show that ¦E¦ = 4/15n5 where E is the error made in order 5.Make an octave code to integrate ex with respect to dx from 0 to 1, by Simpson’s ⅓ rule. Divide the limits into 6 equal parts.
- How large should n be to guarantee that the Simpsons Rule approximation to the integral of (-x^4+16x^3-90x^2+5x-3) dx from bounds 3 to 5 is accurate to within 0.1. n=30. For what value of b does the integral x2 dx equal lim n approaches infinityConsider y=xsin(pi)x over [0,2] Verify the mean value that applies and find all values c satisfying it.
