Chapter 13: Q. 30 (page 1083)

Evaluating triple integrals: Each of the triple integrals that follows represents the volume of a solid. Sketch the solid and evaluate the integral.
$\int_{0}^{2 π} \int_{0}^{2} \int_{0}^{5} r d z d r d θ$

Short Answer

Expert verified

$\int_{0}^{2 π} \int_{0}^{2} \int_{0}^{5} r d z d r d θ = 20 π$

Step by step solution

Given

We have to find the volume by using the triple integral.

\int_{0}^{2 π} \int_{0}^{2} \int_{0}^{5} r d z d r d θ

Evaluate the integral

$V = \int_{0}^{2 π} \int_{0}^{2} [\int_{0}^{5} r d z] d r d θ V = \int_{0}^{2 π} [\int_{0}^{2} 5 r d r] d θ V = 5 \int_{0}^{2 π} {[\frac{r^{2}}{2}]}_{0}^{2} d θ V = 5 \times 2 \int_{0}^{2 π} d θ V = 10 (2 π - 0) V = 20 π cubic units$

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Evaluating triple integrals: Each of the triple integrals that follows represents the volume of a solid. Sketch the solid and evaluate the integral.
$\int_{0}^{2 π} \int_{0}^{2} \int_{0}^{5} r d z d r d θ$

Short Answer

Step by step solution

Given

Evaluate the integral

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Evaluating triple integrals: Each of the triple integrals that follows represents the volume of a solid. Sketch the solid and evaluate the integral. ∫02π∫02∫05rdzdrdθ

Short Answer

Step by step solution

Given

Evaluate the integral

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

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Geometry

Theoretical and Mathematical Physics

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Statistics

Study anywhere. Anytime. Across all devices.

Evaluating triple integrals: Each of the triple integrals that follows represents the volume of a solid. Sketch the solid and evaluate the integral.
$\int_{0}^{2 π} \int_{0}^{2} \int_{0}^{5} r d z d r d θ$