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Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

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BuyFindarrow_forward

Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

Finding the Area of a Polar Region In Exercises 7-18, Find the area of the region.

Two petals of   r = 4 sin 3 θ

To determine

To calculate: The value of area of two petal of polar equation r=4sin3θ.

Explanation

Given:

The polar equation is r=4sin3θ.

Calculation:

Shaded section of two petal circumscribed by the curve r=4sin3θ is shown below:

Use the following steps in Ti-83 calculator to plot the graph:

Step1: Press MODE Key and select POL mode.

Step2: Press (Y=) Key.

Step3: Press r1=4sin3θ

Step4: Now press the [GRAPH] key and the graph is found:

From the figure, it can be seen that pf polar region lies among 0 to 2π.

The section for polar axis is drawn out for one petal is 0θπ3

Substitute 4sin3θ for r, π3 for β and 0 for α

The area of shaded section bounded by graph of r=f(θ) between the radial lines θ=α and θ=β.

So,

A=12αβ[f(θ]2.dθ

Substitute these values in above formula and get,

A=120π3[4sin3θ]2

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P-83RECh-10 P-84RECh-10 P-85RECh-10 P-86RECh-10 P-87RECh-10 P-88RECh-10 P-89RECh-10 P-90RECh-10 P-91RECh-10 P-92RECh-10 P-93RECh-10 P-94RECh-10 P-95RECh-10 P-96RECh-10 P-97RECh-10 P-98RECh-10 P-99RECh-10 P-100RECh-10 P-101RECh-10 P-102RECh-10 P-103RECh-10 P-104RECh-10 P-105RECh-10 P-106RECh-10 P-107RECh-10 P-108RECh-10 P-109RECh-10 P-110RECh-10 P-111RECh-10 P-112RECh-10 P-113RECh-10 P-114RECh-10 P-115RECh-10 P-116RECh-10 P-117RECh-10 P-118RECh-10 P-119RECh-10 P-120RECh-10 P-121RECh-10 P-122RECh-10 P-123RECh-10 P-124RECh-10 P-125RECh-10 P-126RECh-10 P-1PSCh-10 P-2PSCh-10 P-3PSCh-10 P-4PSCh-10 P-5PSCh-10 P-6PSCh-10 P-7PSCh-10 P-8PSCh-10 P-9PSCh-10 P-10PSCh-10 P-11PSCh-10 P-12PSCh-10 P-13PSCh-10 P-14PSCh-10 P-15PSCh-10 P-16PSCh-10 P-17PS

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