Convert the following integral to an integral in polar coordinates. Je V x2 + y2 d...
10. Evaluate the given integral by changing to polar coordinates. JJR x2 + y2" where R is the region that lies between the circles x2 + y2 = a2 and x2 + y2 = 62 with 0 <a<b.
Convert the equation to polar coordinates. x2 + y2 = 7y + X Sketch the graph.
(1 point) Using polar coordinates, evaluate the integral ST sin(x2 + x>)dA where Ris the region 1 5x2 + y2 549. 1.080
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.
Is the following statement "If we use the change of variables with polar coordinates to evaluate the double integral +3x)dA where D is the region in the third quadrant between x2 + y2 = 1 and x2 + y2 =9 after the evaluation of the inner integral we have L 05/2 20sin?(Q) +26cos(9)de." true or false? Select one: O True OO False
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)...
please with graph (3pts) Use polar coordinates to setup V x2 + y2dA, where D is J J(D) bounded by y= Vx– x2, y = 0 and y = x V3.
Evaluate the iterated integral Sa Wa?-? (x2 + y2); dxdy that is given in cartesian coordinates by converting to polar coordinates.
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...