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Chapter 13: Q 8 (page 1066)

To convert from cylindrical to rectangular coordinates:

x=____,y=____,z=____

Short Answer

Expert verified

x=蚁cos胃y=蚁sin胃z=z

Step by step solution

01

Step 1:Given information

Givenx,y,zare rectangular coordinates and蚁,胃,zare cylindrical coordinates

02

Step 2:Simplification

蚁,胃,zare cylindrical coordinates and x,y,zare rectangular coordinates

The relation is as below:

From the figure

cos胃=x蚁

role="math" localid="1653036479004" 鈬�x=蚁cos胃

Similarly

sin胃=y蚁

鈬�y=蚁sin胃

And from the figure we can observez=z

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Most popular questions from this chapter

Use Definition 13.4to evaluate the double integrals in Exercises 29鈥�32.

鈭�Rxy3dA

whereR={(x,y)鈭�-2鈮�x鈮�2&-1鈮�y鈮�1}

Expressthesum25+26+27+28+45+46+47+48usingdouble-summationnotation.

Identify the quantities determined by the integral expressions in Exercises 19鈥�24. If x, y, and z are all measured in centimeters and 蚁(x, y,z) is a density function in grams per cubic centimeter on the three-dimensional region , give the units of the expression.

鈭�惟鈥�z蚁(x,y,z)dV

In Exercises 45鈥�52, rewrite the indicated integral with the specified order of integration.

Exercise 41 with the order dy dx dz.

Explain why using an iterated integral to evaluate a double integral is often easier than using the definition of the double integral to evaluate the integral.
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