Cartesian to polar coordinates Sketch the given region of
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- I sin Using polar coordinates, evaluate the integral sin(x² + y²)dA where R is the region 16 ≤ x² + y² ≤ 81.arrow_forwardQ\ Evaluate the iterated integral by converting to polar coordinates V2x-x2 Vx2 + y2 dy dxarrow_forwardUsing polar coordinates, evaluate the integral sin(x? + y?)dA where R is the region 16 < x2 + y² < 25.arrow_forward
- Determine 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_forwardUsing polar coordinates, evaluate the integral sin(r + y?)dA where R is the region 16 < a² + y? < 49.arrow_forward(2) Evaluate the iterated integral by converting to polar coordinates. 2 V8-y2 x² + y² dx dy o yarrow_forward
- 42. Converting to a polar integral Evaluate the integral dx dy. (1 + x² + y²)²arrow_forward(b) Find the value of the following integrals: 1- dz, y is the triangle with vertices at the points z-51, (2) +z-2) z 31, z 2. %3D -7 2-2 sec z dz, y is the triangle with vertices at the points z=- 5. -i,z=i.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
- A 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_forwardO Choose the correct region of integration (x² + y²) dy dx. Assume that in each figure, the horizontal axis is the x-axis and the vertical axis is the y-axis. O 100-x² 10 10 100-x² Evaluate 10 (Use symbolic notation and fractions where needed.) f(r, 0) dr d0 = O (x² + y²) dy dx by changing to polar coordinates.arrow_forwardUsing polar coordinates, evaluate the integral || J sin sin(x ² + y²)dA where R is the region 16 ≤ x² + y² ≤ 25. Rarrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,