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Evaluate the following double integral by converting to polar coordinates. This question requires a graph. 4...
2. Sketch the region of integration, and then evaluate the integral by first converting to polar coordinates. 1 V2-x2 (x + y)dydx
Double Intergals in Polar Coordinates: 4. Use polar coordinates to find the volume of the solid that is bounded by the paraboloids z = 3x^2 + 3y^2 and z = 4 ? x^2 ? y^2. 5. Evaluate by converting to polar coordinates ? -3 to3 * ? 0 to sqrt(9-x^2) (sin(x^2 +y^2) dydx 6. Evaluate by converting to polar coordinates: ? 0 to 1 * ? -sqrt(1-y^2) to 0 (x^2(y)) dxdy
Evaluate the iterated integral by converting to polar coordinates points) | sin(x² + y2)dydx T SHARE Y COMO
please answer both questions bex Use a double integral in Polar Coordinates to find the area of the rectangular region bounded by x=0,x=1.-O.y-1, HTML Editore BIVA-AIXE 3 1 X X, SE Solve the following double integral using Polar Coordinates. x2 + y dydx HTML Editor
7. Evaluate the following integral by converting to polar coordinates: S], 127 (2x – 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. 8. Find the surface area of the portion of the plane 3x + 2y +z = 6 that lies in the first octant. 9. Use Lagrange multipliers to maximize and minimize f(x, y) = 3x + y...
Evaluate the iterated integral by converting to polar coordinates
1. Use polar coordinates to evaluate the double integral dA z2 +y where R is the region in the first quadrant bounded by the graphs x = 0, y = 1, y=4, and y V3z. 1. Use polar coordinates to evaluate the double integral dA z2 +y where R is the region in the first quadrant bounded by the graphs x = 0, y = 1, y=4, and y V3z.
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.
Using polar coordinates, evaluate the integral so Som x(x2 + y²) dydx. Be careful to check that the limits of integration you use correspond to the region under consideration.