Draw the integration area/region of the integral in the figure
Saded region is the required region
Draw the integration area/region of the integral in the figure S} f(x,y)dA= Els 2 22.00 f(x,y)...
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.
2 1 2 X -2 FIGURE 3. Figure for Problem 6. 6. (4 pts) Consider the double integral V2 2-y2 (2? + y) dA= (32 + y) dx dy + (x2 + y) dx dy. 2-y? (a) ketch the region of integration R in Figure 3. (b) By completing...
pl pl-y The figure below shows the region of integration for the integral [ f(, y, z) dz dy dx. Jo Jo Jo Rewrite this integral as an equivalent iterated integral in the five other orders. z=1-y y=vx 0 1 y
11-x1-x 11. The figure shows the region of integration for the integral S SAx,y,z)dydzds .Rewrite this integral 0 0 in the five other orders. 08 o6 06 04 06 02 02
Evaluate the double integral || f(x, y) dA over the region D. JU f(x, y) = 6x + 9y and D = {(x, y)SXS 1, x3 sy s x3 + 1}
2. Sketch the region of integration, and then evaluate the integral by first converting to polar coordinates. 1 V2-x2 (x + y)dydx
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)...
Sketch the region of integral integration only of integration and evaluate the integral by som S (9) sin (9) dy doc 49 4) Find all absolute extrema of f(x,y,z) - 2r + y +32° subject to 2r-3y-4 Identify any extrema you find as a maximum or a minimum. (10 pts)
Suppose R is the shaded region in the figure, and f(x,y) is a continuous function on R. Find the limits of integration for the following iterated integrals. BD (a) [f $12,9)da = S, "Lº f12, y) dy de PH dA= JE JG f(x,y) dc dy I
Reverse the order of integration in the following integral. 6 24 - 4x s s f(x,y) dy dx y = 24 - 4x 0 0 X Reverse the order of integration. f(x,y) dx
Let R be the region bounded by x + y=1, x - y=1, x+y=3, x-y=-1 evaluate the integral
s(x+ y)2sen2 (x - y)dA
s(x+ y)2sen2 (x - y)dA