8 = = ₁ [(4 + +²) "00 (4 + + ²)] cos i- n the limit as n → ∞o as a definite integral, that is provide a, b and f(x) in the expression [ f(x) dx. Given R₂ a = b = , f(x) = express
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- Prove the conjecture made in the previous exercise.Express as a definite integral the limit as x approaches infinite of 1/n[(1/n)^2 + (2/n)^2 +...+ ((n-1)/n)^2]In this problem you will calculate the area between f(x)=2x^2 and the x-axis over the interval [0,5] using a limit of right-endpoint Riemann sums
- Suppose that f is an integrable function on R (real numbers). How do you show that the integral of f(x) exp(x2/k) converges to the integral of f(x) as k goes to infinity? Here exp() denotes the exponential function with base e.Determine the integral of xydydx using the inner limit = 2x^2 to (1+x) and outer limit = 0 to 1.Use simpson's 1/3 rules with n=8 to evaluate the integral of lower limit 1 and upper limit 5 dx/x(x+2)