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Write an iterated integral to evaluate the integral || 2?;} dA where R is the triangular...
Evaluate the given double integral by changing it to an iterated integral. xy dA; S is the triangular region with vertices (0,0), (10,0), and (0,7) O 35 12 0 1225 6 245 12 175 6
Evaluate the double integral I = Slo xy dA where D is the triangular region with vertices (0,0), (1,0), (0,6).
1. An iterated double integral that is equivalent to *** dx + ry dy JOR 3. Use Groen's Theorem to set up an iterated double integral equal to the line integral $+eva) dx +(2+ + cow y) dy where is the boundary of the region enclosed by the parabolas y rand 1 = y2 with positive orientation. This yields: A. where R is the triangular region with vertices (0,0),(1,0) and (0,1) is: A B. B. So ['(2-z) dr de SL...
10. Consider the triangular region R with vertices (0.0) (a) (4 points) Sketch the triangular region R. Vertices (0.0), (0,2), and (4,0) 3/ lebel up, but do not evaluate, an integral for the volume of the solid obtained by rotating the triangular region R abo al (c) (4 points) Set up, but do not evaluate, an integral for the volume of the described solid. The base is the triangular region R. The cross-sections perpendicular to the r-axis are semi-circles with...
please write neatly and no script! 7. (10 points) For the following iterated integral, sketch the region of integration, then switch the order of integration and evaluate the new iterated integral. 1 •1/2 SL e-22 dx dy. y/2
16. o integrad [**** The triple da dy dz describes the solid pictured at right. Rewrite as an equivalent triple integral in the following orders (DO NOT EVALUATE): 31 (a) dy dz dx (b) du dz dy 2. 16-2 21. Given dy da, 16- (a) Sketch the region of integration and write an equivalent iterated integral in the order dx dy. (You do not need to evaluate it!) (b) Now write it as an equivalent iterated integral in polar coordinates....
Consider the region R shown in the figure and write an iterated integral of a continuous function over R. Choose the correct iterated integral below OA Oc. OD JJ fx.y) dy dx S Study de Consider the region R shown in the figure and write an erated integral a continuous function for Choose the correct terated integral below JJ Roxy) dy dx JJ x) dx dy
1) Given the following iterated integral. ex/Y DA R = y = 4x, y = -xy = 8 a) (0.75 point) Sketch the bounded region R. Label your graph. b) (1.25 point) Evaluate the definite integral with the given function over the bounded region R.
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 integration R in Figure 3.(b) By completing the limits and integrand, set up (without evaluating) the integral in polar coordinates.∫R(x2+y)dA=∫∫drdθ.7. (5 pts) By completing the limits and integrand, set up (without evaluating) an iterated inte-gral which represents the volume of the ice cream cone bounded by the cone z=√x2+y2andthe hemisphere z=√8−x2−y2using(a) Cartesian coordinates.volume =∫∫∫dz dxdy.(b) polar coordinates.volume =∫∫drdθ. -1 -2 FIGURE 3. Figure for Problem 6. 6. (4 pts)...
ST sy +27*dylv Sketch the region R of integration and write as in iterated integral in the order dxdy. Do not evaluate the integral.