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MATH-241-04-2228
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Hand_In_Week_6_M241_F2022.pdf
In cylindrical form for finding the total mass of E. Show work for finding limits of integration and integrand. Do not evaluate.
5. E is bounded above by the surface r^2 + 2 = 16, below by the plane z = 0, and inside the surface Ï = 4sin(θ). The density is Ï = z.
MATH-241-04-2228 -
Calculus IV Fall Quarter 2022
6. E is bounded above by the surface 2 + y^2 + z^2 = 9 and below by the surface 2 + y^2 = 22 with z ≥ 0. The density is Ï = T.
7. Convert the following triple integral in rectangular form to its equivalent cylindrical form. Show work for finding limits of integration and integrand and also sketch the region of integration. ∫∫∫ (x^2 + y^2) xz dz dx dy / 12√(x^2 + y^2)
Home Course Modules
For questions 8 to 9, sketch the region E and then set up appropriate triple integral(s) in spherical form for finding the total mass of E. Show work for finding limits of integration and integrand. Do not evaluate.
@] Syllabus
Modules
2 + y^2 8. E is inside the surface 2 + y^2 + z^2 = 9 and in between z = √(x^2 + y^2) and Ï = √(x^2 + y^2). The density is Ï = 2y^2
Grades
9. E is inside the surface 2 + y^2 + z^2 = 16 and outside the surface x^2 + 2 = 4. The density is Ï = e.
10. Convert the following triple integral in rectangular form to its equivalent spherical form. Show work for finding limits of integration and integrand and also sketch the region of integration.
∫∫∫ (x^2 + 2) dz dy dx / √(x^2 + y^2)
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