Cartesian to polar coordinates Sketch the given region of
28.
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- Evaluate the iterated integral by converting to polar coordinates. 4 *V16 – x2 e-x² - y² dy dx Need Help? Read Itarrow_forwardEvaluate the double integral changing to polar coordinates. 11 (² (2x - y) dA, where R is the region in the first quadrant enclosed by the circle x² + y² Answer: = 25 and the lines x = 0 and y = x, byarrow_forwarda) Change the following double integral from Cartesian to polar coordinate & evaluate the integral: x=1 y=/1-x2 (x2 + y?) dydx x=-1 y=-V1-x2arrow_forward
- 42. Converting to a polar integral Evaluate the integral dx dy. (1 + x² + y²)²arrow_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_forwardEvaluate the iterated integral by converting to polar coordinates. /1 - x² -x2 (x2 + y2)3/2 dy dx dr de =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_forwardUse double integration in Polar coordinates to find the shaded area (the area inside the rose r = 2 sin(20) and outside the circles r 2 sin(0) and r = 2 cos(0)). 2.5 Useful formula: r-2 sin(0) sin (20) = 2 sin(0) cos(0) -2 sin(20) 45 r-2 cos(0)arrow_forward
- 2. Find the volume of the solid bounded by the sphere x² + y² + =² = 6_and the paraboloid = =x² + y° . 6V6-11 Volume = 27 3 Using a triple integral, find the volume of the region outside the sphere xr² +y² +(= -1)² = 1, inside the sphere x + y² + 3. = 4, and bounded below by - = 0.(Volume = 47)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(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_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,