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-1 -2 FIGURE 3. Figure for Problem 6. 6. (4 pts) Consider the double integral V2 /2-y² + = (x2 + y) dx dy + + y) do dy. 2-y2 6. (4 pts) Consider the double integral∫R(x2+y)dA=∫10∫y−y(x2+y)dxdy+∫√21∫√2−y2−√2−y2(x2+y)dxdy.(a) Sketch the region of integrationRin Figure 3.(b) By completing the limits and integrand, set up (without evaluating) the integral in polar coordinates.

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I am giving answer of the first question(question number 6) with its two parts . Thank you.

Solution:- √2-12 Vz y Jenay)da = (x²+4) dx dy + (x² + y) dady. R o ay 1 J2-42 For the is the first double integral region givthe lines y=1 (CD) y=52 (EF) Region R2 is given in Block coloured shaded Region The the graph region. by the total Hence R isY CA A 1 x=y x=-4 2 E E y=12F y=ly D c4 2 mx too -2 - 1 X! -1 3279²=2 -2 y(9) Hence the R is given by R 2 region 3 (2,8) : -J2-g2224 2-y2, yzacy? x² + y2 = 2. That is - 6 in Polar Coordinate x=rcoso.=> x²+y rero cos + sino) s poca - 1 Decembrie r(0 cose +sino) & drdo (rcosho + sino) do do + O O This is the integral in Pola

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6. (4 pts) Consider the double integral∫R(x2+y)dA=∫10∫y−y(x2+y)dxdy+∫√21∫√2−y2−√2−y2(x2+y)dxdy.(a) Sketch the region of integrationRin Figure 3.(b) By completing...
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