# 5.3 pt 3 - 5.3 The Dauble Imegral Over Regions 1 3:2 15(32...

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Unformatted text preview: 5.3 The Dauble Imegral Over Regions 1 3:2 15. // (32+xy—yzjdg/rﬁ‘ c? 0 . 4 5.3 14. ff 3d\$dy 2 y3—1 l a: 15. f / [x+y)2dydm I] x7 I 3y 16. f / ex+ydxdy o a In Exercises 17—20, sketch the region of integration, interchange the order, and evaluate. 1 1 be“. 0 a: 9—" ' l hhHH\ «x2 cos .1: ' \ 18. f / cos a: dydx 0 o ‘. 1 1 ; __ . .. .4 __ 19' / / (“ﬁmdy \ f: D 1.1. J __ - 4 1/5 20. f f {\$2 + y2)dyd\$ 1 1 In Exercises 21—24, integrate the function f over the region D. 2]. ﬁx, 3;) = a: — y; D is the triangle with vertices (0,0), (1,0), and (2,1). 22. f[x,y) = x3y+ cos 2:;D is the triangle deﬁned byﬂ S a: 5 1172, 0 5 y S a. 23. ﬂay) :2 {x2 + Fla-y2 + 2);!) is the region bounded by the graph of y = ~w2+x, the x axis, and the lines at = D and a: = 2 24. f(a:, y) = sinzcos y; D is the pinwheel in Figure 5.3.1]. dmdy 2.IfD= —1,1 —1,2, t s <. 5 [ ]x[ lshowthal fA\$2+y2+1_6 26. Iff(:r, y) 2 351“ (”+1”) and D = {—rr,1r] x [—ww], show that 1 1 _(.__ <_ e ~4W2Mfiw,yldx4-e 27. Show that evaluating fo dxdy, where D is a region of type I, reproduces the formula for the area betwe en curves from onewariable calculus. 305 ...
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