Q12.10P In Problem 4 to 13, identify eac... [FREE SOLUTION]

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Chapter 11: Q12.10P (page 559)

In Problem 4 to 13, identify each of the integral as an elliptic (see Example 1 and 2). Learn the notation of your computer program (see Problem 3) and then evaluate the integral by computer.
10. ${鈭�}_{0}^{\frac{蟺}{4}} \frac{1}{\sqrt{4 - s i n^{2} 胃}} d 胃$ .

Short Answer

Expert verified

The value of integral in elliptic form is $\frac{1}{2} F (\frac{蟺}{4}, \frac{1}{2}) 鈮� 0.40218$ .

Step by step solution

Given Information

The given integral is ${鈭�}_{0}^{\frac{蟺}{4}} \frac{1}{\sqrt{4 - \sin^{2} 胃}} d 胃$ .

Definition of elliptic form

The elliptic form of the integral is defined as $F (\frac{蟺}{2}, k) = {鈭�}_{0}^{\frac{蟺}{2}} \frac{1}{\sqrt{1 - k^{2} s i n^{2} 胃}} d 胃$ .

Find the value of Integral

Let the given integration is ${鈭�}_{0}^{\frac{蟺}{4}} \frac{1}{\sqrt{4 - \sin^{2} 胃}} d 胃$ .

Factor out 4 the equation becomes as follows,

$\begin{array}{rcl} l & = & {鈭�}_{0}^{\frac{蟺}{4}} \frac{1}{\sqrt{4 (1 - \frac{1}{4} \sin^{2} 胃)}} d 胃 \\ = & {鈭�}_{0}^{\frac{蟺}{4}} \frac{1}{4 \sqrt{(1 - \frac{1}{4} \sin^{2} 胃)}} d 胃 \end{array}$

The formula for the beta function is $\begin{array}{rcl} F (\frac{蟺}{2}, K) & = & {鈭�}_{0}^{\frac{蟺}{2}} \frac{1}{\sqrt{1 - k^{2} \sin^{2} 胃}} d 胃 \end{array}$ .

Equate the above equation with the value of I, and the value of I becomes follows,

$\begin{array}{rcl} l & = & \frac{1}{2} {鈭�}_{0}^{\frac{蟺}{4}} \frac{1}{\sqrt{1 - {(\frac{1}{2})}^{2} \sin^{2} 胃}} d 胃 \\ l & = & \frac{1}{2} F (\frac{蟺}{4}, \frac{1}{2}) \\ l & 鈮� & 0.40218 \end{array}$

The value of integral in elliptic form is $\begin{array}{rcl} \frac{1}{2} F (\frac{蟺}{4}, \frac{1}{2}) & 鈮� & 0.40218 \end{array}$ .

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91影视

In Problem 4 to 13, identify each of the integral as an elliptic (see Example 1 and 2). Learn the notation of your computer program (see Problem 3) and then evaluate the integral by computer.
10. ${鈭�}_{0}^{\frac{蟺}{4}} \frac{1}{\sqrt{4 - s i n^{2} 胃}} d 胃$ .

Short Answer

Step by step solution

Given Information

Definition of elliptic form

Find the value of Integral

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Most popular questions from this chapter

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91影视

In Problem 4 to 13, identify each of the integral as an elliptic (see Example 1 and 2). Learn the notation of your computer program (see Problem 3) and then evaluate the integral by computer.10. 鈭�0蟺414-sin2胃d胃.

Short Answer

Step by step solution

Given Information

Definition of elliptic form

Find the value of Integral

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Atoms and Radioactivity

Force

Physical Quantities And Units

Fields in Physics

Wave Optics

Quantum Physics

Study anywhere. Anytime. Across all devices.

In Problem 4 to 13, identify each of the integral as an elliptic (see Example 1 and 2). Learn the notation of your computer program (see Problem 3) and then evaluate the integral by computer.
10. ${鈭�}_{0}^{\frac{蟺}{4}} \frac{1}{\sqrt{4 - s i n^{2} 胃}} d 胃$ .