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A flat plate has an area D specified by the constraints y> 0 and 1 <...
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.
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.
Q3(a) Let W be the region above the sphere x2 + y2 + z2 = 6 and below the paraboloid z = 4 - x2 - y2 as shown in Figure Q5(a) below: Z=4-x-y? x2 + y + z = 6 Figure Q3(a) (i) Find the equation of the projection of Won the xy-plane. (ii) Compute the volume of W using polar coordinates. [16 marks] (b) Using double integral in polar coordinates, compute the following: $$*** (2x+3y) dedy [7 marks]...
Please do #2
40 1. 16 pts) Evaluate the integral( quadrant enclosed by the cirle x + y2-9 and the lines y - 0 and y (3x-)dA by changing to polar coordinates, where R is the region in the first 3x. Sketch the region. 2. [6 pts) Find the volume below the cone z = 3、x2 + y2 and above the disk r-3 cos θ. your first attempt you might get zero. Think about why and then tweak your integral....
Evaluate the given integral by changing to polar coordinates. ∫∫R(4x − y) dA, where R is the region in the first quadrant enclosed by the circle x2 + y2 = 4 and the lines x = 0 and y = x.
Can you please solve both of
these problems?
Evaluate the given integral by changing to polar coordinates. 9(x + y) dA where R is the region that lies to the left of the y-axis between the circles x2 + y2 = 1 and x2 + y2 = 4. , -378 Need Help? Read It Master It Talk to a Tutor -11 points v SCALCET8 15.3.511.XP. Evaluate the given integral by changing to polar coordinates. Il V25 – x2 + y2...
D . Problem 4. A lamina lies in the first quadrant and is enclosed by the circle x2 +y2 = 4 and the lines x = 0 and y = 0. The density function of the lamina is equal to p(x, y) = V x2 + y2. Use the double integral formula in polar coordinates, S/ s(8,y)dx= $." \* fcr cos 6,r sin Øyrar] de, Ja [ Ꭱ . to calculate (1) the mass of the lamina, m = SSP(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...
1. (4 points) Evaluate the double integral on the given domain D xy where D={(x,y):25x54,15ys3} 2. (4 points) Evaluate the double integral on the given domain S dxdy © 1(x2 + y2)3 where D=(x,y):15x2 + y2 <4, yzo}
Problem 6 [5 points] |(y ( y-dan- 0.708 Set up an equation with a double Integral in polar coordinates to find a such that the volume inside the hemisphere z 16-x-yi and outside the cylinder x2 + y2 = a 2 is one-half the volume of the hemisphere. Do not solve it.
Problem 6 [5 points] |(y ( y-dan- 0.708 Set up an equation with a double Integral in polar coordinates to find a such that the volume inside the...