Chapter 9: Q. 17 (page 756)

Find a definite integral expression that represents the area of the given region in the polar plane and then find the exact value of expression
The region bounded enclosed by the spiral $r = θ$ and the x-axis on the interval $0 \leq θ \leq π$

Short Answer

Expert verified

The integral can be given as $\frac{1}{2} \int_{0}^{π} θ^{2} d θ$ . The exact value of integral can be given as 5.165 units

Step by step solution

Given information

We are given an equation of spiral as $r = θ$

Evaluate

The area can be given as

$A = \frac{1}{2} \int_{0}^{π} r^{2} d θ A = \frac{1}{2} \int_{0}^{π} θ^{2} d θ A = \frac{1}{2} (10.33) A = 5.165 u n i t$

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Find a definite integral expression that represents the area of the given region in the polar plane and then find the exact value of expression
The region bounded enclosed by the spiral $r = θ$ and the x-axis on the interval $0 \leq θ \leq π$

Short Answer

Step by step solution

Given information

Evaluate

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Find a definite integral expression that represents the area of the given region in the polar plane and then find the exact value of expressionThe region bounded enclosed by the spiralr=θand the x-axis on the interval0≤θ≤π

Short Answer

Step by step solution

Given information

Evaluate

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Mechanics Maths

Applied Mathematics

Calculus

Decision Maths

Pure Maths

Study anywhere. Anytime. Across all devices.

Find a definite integral expression that represents the area of the given region in the polar plane and then find the exact value of expression
The region bounded enclosed by the spiral $r = θ$ and the x-axis on the interval $0 \leq θ \leq π$