Q. 27 In exercise 26-30 Find a definit... [FREE SOLUTION]

Chapter 9: Q. 27 (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 $r = e^{胃} f o r 0 鈮� 胃鈮� 2 蟺$

Short Answer

Expert verified

The integral can be given as $\sqrt{2} {鈭�}_{0}^{2 蟺} e^{胃} d 胃$ and the length of the polar curve can be given as $40.36 u n i t s$

Step by step solution

Given information

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

We find the definite integral and evaluate it

We know that length of polar curve can be given as

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

We are given

$r = e^{胃} r' = e^{胃}$

On substituting the values we get,

${鈭�}_{0}^{2 蟺} \sqrt{e^{2 胃} + e^{2 胃}} d 胃 = {鈭�}_{0}^{2 蟺} \sqrt{2 e^{2 胃}} d 胃 = \sqrt{2} {鈭�}_{0}^{2 蟺} \sqrt{e^{2 胃}} d 胃 = \sqrt{2} {鈭�}_{0}^{2 蟺} e^{胃} d 胃 = \sqrt{2} (e^{2 蟺} - 1)$

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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
the spiral $r = e^{胃} f o r 0 鈮� 胃鈮� 2 蟺$

Short Answer

Step by step solution

Given information

We find the definite integral and evaluate it

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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 integralthe spiralr=e胃for0鈮�胃鈮�2蟺

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

Discrete Mathematics

Mechanics Maths

Calculus

Statistics

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 $r = e^{胃} f o r 0 鈮� 胃鈮� 2 蟺$