Chapter 9: Q. 38 (page 775)

Areas of regions bounded by polar functions: Find the areas of the following regions. The area bounded by one loop of $r^{2} = 4 \cos 2 θ$ .

Short Answer

Expert verified

The area bounded by one loop is $2 units$

Step by step solution

Given information

$r^{2} = 4 \cos 2 θ$

Area

The graph of the given function is,

The area bounded by one loop is,

$A = \frac{1}{2} \int_{α}^{β} r^{2} d θ A = \frac{1}{2} \int_{- \frac{π}{4}}^{\frac{π}{4}} 4 \cos 2 θ d θ A = 2 {(\frac{\sin 2 θ}{2})}_{- \frac{π}{4}}^{\frac{π}{4}} A = 2 (\frac{\sin 2 (\frac{π}{4})}{2} - \frac{\sin 2 (- \frac{π}{4})}{2}) A = 4 (\frac{1}{2} + \frac{1}{2}) A = 2 units$

The required area is $A = 2 units$

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Areas of regions bounded by polar functions: Find the areas of the following regions. The area bounded by one loop of $r^{2} = 4 \cos 2 θ$ .

Short Answer

Step by step solution

Given information

Area

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Areas of regions bounded by polar functions: Find the areas of the following regions. The area bounded by one loop of r2=4cos2θ.

Short Answer

Step by step solution

Given information

Area

One App. One Place for Learning.

Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

Areas of regions bounded by polar functions: Find the areas of the following regions. The area bounded by one loop of $r^{2} = 4 \cos 2 θ$ .