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a) Write the iterated integral in rectangular coordinates that gives the surface area of the graph...
please write neatly and no script! 8. (10 points) (a) Using rectangular coordinates, set up an iterated integral that represents the volume of the solid bounded by the surfaces z = x2 + y2 +3, z = 0, and x2 + y2 = 1. (b) Evaluate the iterated integral in (a) by converting to polar coordinates.
3. Convert the integral from rectangular coordinates to both cylindrical an spherical coordinates, and evaluate the simplest iterated integral. 1 1-y2 3. Convert the integral from rectangular coordinates to both cylindrical an spherical coordinates, and evaluate the simplest iterated integral. 1 1-y2
For the described solid S, write the triple integral f(x,y, z)dV as an iterated integral in (i) rectangular coordinates (x,y, z); (ii) cylindrical coordinates (r, 0, 2); (iii) spherical coordinates (p, φ,0). a. Inside the sphere 2 +3+224 and above the conezV b. Inside the sphere x2 + y2 + 22-12 and above the paraboloid z 2 2 + y2. c. Inside the sphere 2,2 + y2 + z2-2 and above the surface z-(z2 + y2)1/4 d. Inside the sphere...
Evaluate the iterated integral by converting to polar coordinates points) | sin(x² + y2)dydx T SHARE Y COMO
Evaluate the iterated integral Sa Wa?-? (x2 + y2); dxdy that is given in cartesian coordinates by converting to polar coordinates.
Write as an iterated integral in cylindrical coordinates in the order dOdzdr, but do not evaluate: +(x + y²)zdzdxdy
Evaluate the iterated integral by converting to polar coordinates. pV 32 – v2 V22 + y2 dx dy
A2) Let Sl be the unit circle z2 + y2-l in R2. Let S2 be the unit sphere z2 + y2 + z2-l in R. Let Sn be the unit hypersphere x| + z +--+ z2+1-1 in Rn+1 (a) Write an iterated double integral in rectangular coordinates that expresses the area inside S1. Write an iterated triple integral in rectangular coordinates that expresses the volume inside S2. Write an iterated quadruple integral in rectangular coordinates that expresses the hypervolume inside...
Evaluate the iterated integral by converting to polar coordinates
NOTE: in spherical coordinates the volume is obtained by the sum of 2 iterated integrals Also, please do your best with the handwriting. Thank you very much :) Part 1 Convert the rectangular coordinate integral to cylindrical coordinates and spherical coordinates and evaluate the simplest iterated integral: 13 x dz dy dx 14 x2+ y? dz dy de Part 1 Convert the rectangular coordinate integral to cylindrical coordinates and spherical coordinates and evaluate the simplest iterated integral: 13 x dz...