Q. 45 Use Theorem 9.13 to show that th... [FREE SOLUTION]

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Chapter 9: Q. 45 (page 756)

Use Theorem 9.13 to show that the area of the circle defined by the polar equation $r = a$ is ${蟺补}^{2}$ .

Short Answer

Expert verified

The area of the circle is ${蟺补}^{2}$

Step by step solution

Step 1. Given Information

The given function of the circle is $r = a$ .

Step 2. Use the formula for area of a region bounded by a curve

The region is bounded by the curve $r = a$ .
The region is a circle, so the boundary arcs will be $胃 = 0, 胃 = 2 蟺$ .
So, the area of the region will be calculated as follows:role="math" localid="1649917065658" $\begin{array}{rcl} \frac{1}{2} {鈭�}_{0}^{2 蟺} a^{2} d 胃 & = & \frac{a^{2}}{2} {鈭�}_{0}^{2 蟺} d 胃 \\ = & \frac{a^{2}}{2} 脳 2 蟺 \\ = & {蟺补}^{2} \end{array}$
Hence, the area of the curve is ${蟺补}^{2}$ .

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91影视

Use Theorem 9.13 to show that the area of the circle defined by the polar equation $r = a$ is ${蟺补}^{2}$ .

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Use the formula for area of a region bounded by a curve

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91影视

Use Theorem 9.13 to show that the area of the circle defined by the polar equation r=ais 蟺补2.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Use the formula for area of a region bounded by a curve

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

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Use Theorem 9.13 to show that the area of the circle defined by the polar equation $r = a$ is ${蟺补}^{2}$ .