Chapter 13: Q. 18 (page 1082)

Using polar coordinates to evaluate iterated integrals: Sketch the region determined by the limits of the given iterated integrals, and then evaluate the integrals.
$\int_{π / 2}^{3 π / 2} \int_{1}^{4} r^{3 / 2} d r d θ$

Short Answer

Expert verified

$\int_{π / 2}^{3 π / 2} \int_{1}^{4} r^{3 / 2} d r d θ = \frac{62}{5} π$

Step by step solution

Draw the region.

The region determined by the limits is shown below,

Evaluate the integral

$I = \int_{π / 2}^{3 π / 2} \int_{1}^{4} r^{3 / 2} d r d θ I = \int_{π / 2}^{3 π / 2} {[\frac{r^{\frac{3}{2} + 1}}{\frac{3}{2} + 1}]}_{1}^{4} d θ I = \frac{2}{5} \int_{π / 2}^{3 π / 2} {[r^{\frac{5}{2}}]}_{1}^{4} d θ I = \frac{2}{5} \int_{π / 2}^{3 π / 2} [4^{\frac{5}{2}} - 1^{\frac{5}{2}}] d θ I = \frac{2 \times 31}{5} \int_{π / 2}^{3 π / 2} d θ I = \frac{62}{5} [\frac{3 π}{2} - \frac{π}{2}] I = \frac{62}{5} π$

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Using polar coordinates to evaluate iterated integrals: Sketch the region determined by the limits of the given iterated integrals, and then evaluate the integrals.
$\int_{π / 2}^{3 π / 2} \int_{1}^{4} r^{3 / 2} d r d θ$

Short Answer

Step by step solution

Draw the region.

Evaluate the integral

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Using polar coordinates to evaluate iterated integrals: Sketch the region determined by the limits of the given iterated integrals, and then evaluate the integrals.∫π/23π/2∫14r3/2drdθ

Short Answer

Step by step solution

Draw the region.

Evaluate the integral

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

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Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Using polar coordinates to evaluate iterated integrals: Sketch the region determined by the limits of the given iterated integrals, and then evaluate the integrals.
$\int_{π / 2}^{3 π / 2} \int_{1}^{4} r^{3 / 2} d r d θ$