Q. 29 In exercise 26-30 Find a definit... [FREE SOLUTION]

Chapter 9: Q. 29 (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
$T h e s p i r a l r = e^{伪胃} f o r 0 鈮� 胃鈮� 2 蟺$

Short Answer

Expert verified

The integral can be given as ${鈭�}_{0}^{2 蟺} \sqrt{1 + 伪^{2}} e^{伪胃} d 胃$ and the length of the spiral can be given as $\sqrt{(1 + 伪^{2})} (\frac{e^{2 蟺伪} - 1}{伪})$

Step by step solution

Given information

We are given a spiral with equation $r = e^{伪胃} f o r 0 鈮� 胃鈮� 2 蟺$

Find the integral and evaluate it

We know that

${鈭�}_{0}^{2 蟺} \sqrt{(f {(胃))}^{2} + (f' {(胃))}^{2}} d 胃$

We are given

$r = e^{伪胃} r' = 伪 e^{伪胃}$

Substituting in the formula we get

localid="1650460246282" ${鈭�}_{0}^{2 蟺} \sqrt{e^{2 伪胃} + 伪^{2} e^{2 伪胃}} d 胃 = \sqrt{1 + 伪^{2}} {鈭�}_{0}^{2 蟺} \sqrt{e^{2 伪胃}} d 胃 = \sqrt{1 + 伪^{2}} {鈭�}_{0}^{2 蟺} e^{伪胃} d 胃 = \sqrt{(1 + 伪^{2})} (\frac{e^{2 蟺伪} - 1}{伪})$

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91影视

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
$T h e s p i r a l r = e^{伪胃} f o r 0 鈮� 胃鈮� 2 蟺$

Short Answer

Step by step solution

Given information

Find the integral and evaluate it

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Most popular questions from this chapter

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91影视

In exercise 26-30 Find a definite integral that represents the length of the specified polar curve and then find the exact value of integralThespiralr=e伪胃for0鈮�胃鈮�2蟺

Short Answer

Step by step solution

Given information

Find the integral and evaluate it

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Applied Mathematics

Logic and Functions

Geometry

Mechanics Maths

Theoretical and Mathematical Physics

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
$T h e s p i r a l r = e^{伪胃} f o r 0 鈮� 胃鈮� 2 蟺$