Chapter 5.5, Problem 2ES

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Evaluate the double integral ' √ √ (−2xy² + 3ry) dA R where R = {(x,y)| 1 ≤ x ≤ 3, 2 ≤ y ≤ 4} Double Integral Plot of integrand and Region R N 120 100 80- 60- 40 20 -20 -40 2 T 3 4 5123456 This plot is an example of the function over region R. The region and function identified in your problem will be slightly different. Answer = Round your answer to four decimal places.

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Find Te²+ dydz 0 Write your answer in exact form.

xy² Find -dA, R = [0,3] × [−4,4] x²+1 Round your answer to four decimal places.

Find the values of p for which the series is convergent. P-?- ✓ 00 Σ nº (1 + n10)p n = 1 Need Help? Read It Watch It SUBMIT ANSWER [-/4 Points] DETAILS MY NOTES SESSCALCET2 8.3.513.XP. Consider the following series. 00 Σ n = 1 1 6 n° (a) Use the sum of the first 10 terms to estimate the sum of the given series. (Round the answer to six decimal places.) $10 = (b) Improve this estimate using the following inequalities with n = 10. (Round your answers to six decimal places.) Sn + + Los f(x) dx ≤s ≤ S₁ + Jn + 1 + Lo f(x) dx ≤s ≤ (c) Using the Remainder Estimate for the Integral Test, find a value of n that will ensure that the error in the approximation s≈s is less than 0.0000001. On > 11 n> -18 On > 18 On > 0 On > 6 Need Help? Read It Watch It

√5 Find Lª³ L² y-are y- arctan (+) dy dydx. Hint: Use integration by parts. SolidUnderSurface z=y*arctan(1/x) Z1 2 y 1 1 Round your answer to 4 decimal places.

For the solid lying under the surface z = √√4-² and bounded by the rectangular region R = [0,2]x[0,2] as illustrated in this graph: Double Integral Plot of integrand over Region R 1.5 Z 1- 0.5- 0 0.5 1 1.5 205115 Answer should be in exact math format. For example, some multiple of .