7. Evaluate the following integral by converting to polar coordinates: S], 127 (2x – y)dA, where...
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.
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.
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.
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.
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.
Use polar coordinates to evaluate the integral where R is the region in in the first quadrant enclosed by the circumference x2+y2=4 and the lines x=0 and y=x SUR (60 - 3y)dA Use coordenadas polares para evaluar la integral JR (6x – 3y)dA donde R es la región en en el primer cuadrante encerrada por la circunferencia za + y2 = 4y las rectas r = Oyy=2. 0-8+12V2 O NO ESTÁ LA RESPUESTA O 16 - 12/2 O 12 -...
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....
9. (12 pts. Use the method of Lagrange multipliers to maximize and minimize f(x, y) =3x + y subject to the constraint x2 + y2 = 10. (Both extreme values exist.)
Q4: Use polar coordinates to evaluate x2 - y2 dA, where R is the region in the first V9- quadrant within the circle x2 + y2-9.
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