Chapter 9: Q. 26 (page 756)

In exercise 26-30 Find a definite integral that represents the length of the specified polar curve and then find the exact value of integral
The spiral $r = θ f o r 0 \leq θ \leq 2 π$

Short Answer

Expert verified

The integral can be given as $\int_{0}^{2 π} \sqrt{1 + θ^{2}} d θ$ and its length is $21.25 u n i t s$

Step by step solution

Given information

We are given a spiral represented by a function $r = θ f o r 0 \leq θ \leq 2 π$

We find the definite integral and evaluate it

We know that length of polar curve can be given as

$\int_{a}^{b} \sqrt{(f {(θ))}^{2} + (f' {(θ))}^{2}} d θ$

We are given $r = θ \frac{d r}{d θ} = 1$

Substituting the above values in the integral we get,

$\int_{0}^{2 π} \sqrt{1 + θ^{2}} d θ$

On solving the integral we get the value as

role="math" localid="1649471467926" $\int_{0}^{2 π} \sqrt{1 + θ^{2}} d θ = 21.25 u n i t s$

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In exercise 26-30 Find a definite integral that represents the length of the specified polar curve and then find the exact value of integral
The spiral $r = θ f o r 0 \leq θ \leq 2 π$

Short Answer

Step by step solution

Given information

We find the definite integral and evaluate it

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In exercise 26-30 Find a definite integral that represents the length of the specified polar curve and then find the exact value of integralThe spiralr=θfor0≤θ≤2π

Short Answer

Step by step solution

Given information

We find the definite integral and evaluate it

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Geometry

Applied Mathematics

Logic and Functions

Probability and Statistics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In exercise 26-30 Find a definite integral that represents the length of the specified polar curve and then find the exact value of integral
The spiral $r = θ f o r 0 \leq θ \leq 2 π$