Cartesian to polar coordinates Sketch the given region of
24.
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- Evaluate the integral by converting to polar coordinates. /8-y? 1 dx dy = V1+x² + y²arrow_forwardUsing polar coordinates, evaluate the integral sin(x? + y?)dA where R is the region 16 < x2 + y² < 25.arrow_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_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_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_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_forwardConverting 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_forward
- 42. Converting to a polar integral Evaluate the integral dx dy. (1 + x² + y²)²arrow_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_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_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,