Cartesian to polar coordinates Sketch the given region of
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- sketch! Convert to polar coordinates to evaluate the double integral is the region in the first quadrant enclosed by x² + y² = 9 and the lines z = 0 and y = r. 11.1² (2x - y) dA, where Rarrow_forwardEvaluate the integral by converting to polar coordinates. /8-y? 1 dx dy = V1+x² + y²arrow_forwardUsing polar coordinates, evaluate the integral sin(r + y?)dA where R is the region 16 < a² + y? < 49.arrow_forward
- I sin Using polar coordinates, evaluate the integral sin(x² + y²)dA where R is the region 16 ≤ x² + y² ≤ 81.arrow_forwardDetermine the y-coordinate of the centroid of the area under the sine curve shown. y y = 3 sin 11 3 --x 11 Answer: y = iarrow_forwardA region R is shown. Decide whether to use polar coordinates or rectangular coordinates and write f(x,y) dA as an integral, where f is an arbitrary continuous function on R. T -2 R IN (3.54.-3.54) Update the values of a, b, c, d and u, v,g, s(u, v), t(u, v) in the box below so that the integral shown is your exact solution. int(int(g(s(u,v), t(u,v)),u,a,b),v,c,d)arrow_forward
- Using polar coordinates, evaluate the integral || J sin sin(x ² + y²)dA where R is the region 16 ≤ x² + y² ≤ 25. Rarrow_forwardCartesian to polar coordinates Evaluate the following integralover the specified region. Assume (r, θ) are polar coordinates.arrow_forward42. Converting to a polar integral Evaluate the integral dx dy. (1 + x² + y²)²arrow_forward
- Converting from Rectangular Coordinates to Spherical Coordinates Convert the following integral into spherical coordinates: y=3 x=√√9-y²z=√√/18-x²-y² , , x=0 y=0 [ (x² + y² + z²) dz dx dy. z=√√/x² + y²arrow_forwardP10) The region R in the xy-plane is bounded by the circles x2 + y2 = 4 and x2 + (y − 2)2 = 4 I. Set up, but do not evaluate, an integral or sum of integrals in Cartesian coordinates that represents the area of R. You may choose the variable of integration freely. II. Set up, but do not evaluate, an integral or sum of integrals using polar coordinates that represents the area of R. See details in image uploaded please.arrow_forwardWhich integral represents the area of R? Choose 1 answer: 5π A sin² (40) de B sin² (40) de © sin² (40) de . sin² (40) de 76 2 π 5TT 49 2 49 4 5TT 49 2 5TT 49 2arrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,