Q12.7P In Problem 4 to 13, identify eac... [FREE SOLUTION]

91影视

Chapter 11: Q12.7P (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.
7. ${鈭�}_{0}^{\frac{5 蟺}{4}} \sqrt{25 - s i n^{2} 胃} d 胃$

Short Answer

Expert verified

The value of integral in elliptic form is $5 E (\frac{5 蟺}{4}, \frac{1}{5}) 鈮� 19.810007$ .

Step by step solution

Given Information

The value of integration is ${鈭�}_{0}^{\frac{5 蟺}{4}} \sqrt{25 - \sin^{2} 胃} d 胃$ .

Definition of elliptic form

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

Find the value of Integral

The value of integration is ${鈭�}_{0}^{\frac{5 蟺}{4}} \sqrt{25 - \sin^{2} 胃} d 胃$ .

Factor out 25, the equation becomes as follows.

$\begin{array}{rcl} l & = & {鈭�}_{0}^{\frac{5 蟺}{4}} \sqrt{25 (1 - \frac{\sin^{2} 胃}{25})} d 胃 \\ = & 5 {鈭�}_{0}^{\frac{5 蟺}{4}} \sqrt{(1 - \frac{\sin^{2} 胃}{25})} d 胃 \end{array}$

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

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

$\begin{array}{rcl} l & = & 5 {鈭�}_{0}^{\frac{5 蟺}{4}} \sqrt{(1 - \frac{\sin^{2 胃}}{25})} d 胃 \\ l & = & 5 E (\frac{5 蟺}{4}, \frac{1}{5}) \\ l & 鈮� & 19.81007 \end{array}$

The value of integral in elliptic form is $\begin{array}{rcl} 5 E (\frac{5 蟺}{4}, \frac{1}{5}) & 鈮� & 19.81007 \end{array}$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

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.
7. ${鈭�}_{0}^{\frac{5 蟺}{4}} \sqrt{25 - s i n^{2} 胃} d 胃$

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

Wave Optics

Fundamentals of Physics

Quantum Physics

Electricity

Fluids

Magnetism

Study anywhere. Anytime. Across all devices.

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.7. 鈭�05蟺425-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

Wave Optics

Fundamentals of Physics

Quantum Physics

Electricity

Fluids

Magnetism

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.
7. ${鈭�}_{0}^{\frac{5 蟺}{4}} \sqrt{25 - s i n^{2} 胃} d 胃$