Q. 8. Consider the three-petaled polar... [FREE SOLUTION]

Chapter 9: Q. 8. (page 755)

Consider the three-petaled polar rose defined by $r = \cos 3 胃$ .Explain why the definite integral localid="1653739667075" $\frac{1}{2} {鈭�}_{0}^{2 蟺} \cos^{2} 3 胃 d 胃$ calculates twice the area bounded by the petals of this rose.

Short Answer

Expert verified

If the area is calculated in the interval $[0, 2 蟺]$ t gives twice the area bounded by the petals of the polar curve $r = \cos 3 胃$

Step by step solution

Given information

The definite integral is $\frac{1}{2} {鈭�}_{0}^{2 蟺} \cos^{2} 3 胃 d 胃$

Consider the polar curve $r = \cos 3 胃$

The objective is to give the reason why the area of the curve 12∫02πcos23θdθ is twice the actual area

The curve $r = \cos 3 胃$ traced twice in the interval $[0, 2 蟺]$

As a result, calculating the area in the interval $[0, 2 蟺]$

It delivers twice the area enclosed by the polar curve's $r = \cos 3 胃$ petals.

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91影视

Consider the three-petaled polar rose defined by $r = \cos 3 胃$ .Explain why the definite integral localid="1653739667075" $\frac{1}{2} {鈭�}_{0}^{2 蟺} \cos^{2} 3 胃 d 胃$ calculates twice the area bounded by the petals of this rose.

Short Answer

Step by step solution

Given information

The objective is to give the reason why the area of the curve 12∫02πcos23θdθ is twice the actual area

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Most popular questions from this chapter

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Probability and Statistics

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Statistics

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91影视

Consider the three-petaled polar rose defined by r=cos3胃.Explain why the definite integral localid="1653739667075" 12鈭�02蟺cos23胃d胃calculates twice the area bounded by the petals of this rose.

Short Answer

Step by step solution

Given information

The objective is to give the reason why the area of the curve 12∫02πcos23θdθ is twice the actual area

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Geometry

Statistics

Decision Maths

Applied Mathematics

Pure Maths

Study anywhere. Anytime. Across all devices.

Consider the three-petaled polar rose defined by $r = \cos 3 胃$ .Explain why the definite integral localid="1653739667075" $\frac{1}{2} {鈭�}_{0}^{2 蟺} \cos^{2} 3 胃 d 胃$ calculates twice the area bounded by the petals of this rose.