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Chapter 12: Multiple Integrals

Expert-verified
Essential Calculus: Early Transcendentals
Pages: 689 - 754
Essential Calculus: Early Transcendentals

Essential Calculus: Early Transcendentals

Book edition 2nd
Author(s) James Stewart
Pages 830 pages
ISBN 9781133112280

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Illustration

305 Questions for Chapter 12: Multiple Integrals

  1. Evaluate the double integral:\begin{gathered}\iint\limits_D {{x^3}dA,} \hfill \\D = \{ x,y)/1 \leqslant x \leqslant e,0 \leqslant y \leqslant lnx\} \hfill \\\end{gathered}

    Found on Page 707

  2. Find the total mass and the center of mass of the lamina. The region is =\(y = {x^2}{\rm{ and }}x = {y^2}\). The density is =\(\rho (x,y) = \sqrt x \).

    Found on Page 720

  3. Question: Evaluate the triple integral

    Found on Page 729

  4. The integral,where \(R = \left( {0,4} \right) \times \left( {0,2} \right)\)represents the volume of a solid. Sketch the solid.

    Found on Page 699

  5. Write the equation in spherical coordinates.

    Found on Page 740

  6. S is the disk given by\begin{aligned}{u^2} + {v^2}1;\; \hfill \\x = au,y = bv \hfill \\ \end{aligned}

    Found on Page 749

  7. Write the equations in cylindrical coordinates.

    Found on Page 734

  8. Determine the solid described by the given inequalities.

    Found on Page 740

  9. Express D as a region of Type 1. And also as a region of type 2. Then evaluate the double integral in 2 ways.

    Found on Page 707

  10. Calculate the iterated integral.

    Found on Page 699

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