B is a rectangular region and its coordinates are (0,0),(5,0),6)3. Please compute S[(x + y)da with...
3. Draw the region D and evaluate the double integral using polar coordinates. dA, D= {(x, y)| x2 + y² <1, x +y > 1} (b) sin(x2 + y2)dA, D is in the third quadrant enclosed by D r? + y2 = 7, x² + y2 = 24, y = 1, y = V3r.
Using Change of Variables..Evaluate ∫∫ R 15y/x dA where R is the region bounded by xy = 2, xy = 6 , y = 4 and y =10 usingthe transformation x=v , y=2u/3v.
Someone please show how to compute the integral of b over the
given region. The answer is in blue but I am not sure how to get
there.
12. D = {0 <<<5,0 < < cos } (a) Sketch the region D T EEN -1 (b) Compute the integral of the function f(x, y) = sin r over the region D. NI-
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
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...
3. Draw the region D and evaluate the double integral using polar coordinates. (a) SI x + y dA, x2 + y2 D= {(x, y)| x2 + y2 < 1, x + y > 1} D (b) ſ sin(x2 + y2)dA, D is in the third quadrant enclosed by m2 + y2 = 71, x2 + y2 = 27, y=x, y= V3x.
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.
-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 (a) Sketch the region of integration R in Figure 3. (b) By completing the limits and integrand, set up (without evaluating)...
3. Evaluate the integral by changing to polar coordinates: SS (x+y) da R Where R is the region in quadrant 2 above the line y=-x and inside the circle x2 + y2 = 2.
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)...
3. Polar Coordinates. (a) Given a rectangular coordinate point (x, y), how do you compute the equivalent polar coordinates: (r, 0)? (b) Given a polar coordinate (r, o), how do you compute the equivalent rectangular coordinate: (x, y)? (c) Consider the drawing in Figure 1. Compute the coordinate of each small circle. (d) What if the circle is centered at the point (cx, cy) (and not the origin). How does the formula change?