15.7: Triple Integrals in Cylindrical Coordinates
15.7: Triple Integrals in Cylindrical Coordinates

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Convert the integral from rectangular coordinates to:
a) Cylindrical Coordinates
b) Spherical Coordinates
Without using an app or calculator, explain which integral is simplest to evaluate. Then evaluate the integral you choose to be the simplest. Neatly show your steps.

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04:12

Convert the integral from rectangular coordinates to both cylindrical and spherical coordinates and evaluate the simplest iterated integral:âˆ«âˆ«âˆ« (2x^2 + y^2 + z^2) dz dy dxâˆ«âˆ«âˆ« (r^2sinÎ¸) dz dr dÎ¸âˆ«âˆ«âˆ« (r^2sinÎ¸) dr dÏ† dÎ¸

05:51

Convert the integral$$\int_{-1}^{1} \int_{0}^{\sqrt{1-y^{2}}} \int_{0}^{x}\left(x^{2}+y^{2}\right) d z d x d y$$to an equivalent integral in cylindrical coordinates and evaluate the result.

01:27

Convert the integral $$\int_{-1}^{1} \int_{0}^{\sqrt{1-y^{2}}} \int_{0}^{x}\left(x^{2}+y^{2}\right) d z d x d y$$$$\begin{array}{l}{\text { to an equivalent integral in cylindrical coordinates and evaluate }} \\ {\text { the result. }}\end{array}$$

04:56

Convert the given integral to an equivalent integral in cylindrical coordinates and evaluate the result: âˆ«âˆ«âˆ« (2s-x^2) { 6âˆš(xz) + y^2 } dz dy dx

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