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Change the order of
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- Determine the exact area of the region bound by the graph of f(x) = −x^2 + 5 and the x-axis on [−1,1] using a right-endpoint Riemann sum.Show that limit t appraoaches infinity integral -t to t x dx =0 This shows that we can’t define integral - infinity to infinity f(x) dx = limit t appraoaches infinity integral -t to t f(x) dxEvaluate the integral of (3x2 + 9y2) dx dy 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 two and lower limit of zero. 10 20 30 40
- 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 1/3 rules with n=8 to evaluate the integral of lower limit 1 and upper limit 5 dx/x(x+2)A function h(x, y) is defined by h(x,y)=(x^2 y)/(〖7x〗^6+y^3 ). Verify the limit over h(x, y) exists at the origin along y = x^2? In either case write also the reason.