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Study Guide for Stewart's Multivar...

8th Edition
Stewart + 1 other
ISBN: 9781305271845

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Chapter
Section
BuyFindarrow_forward

Study Guide for Stewart's Multivar...

8th Edition
Stewart + 1 other
ISBN: 9781305271845
Textbook Problem

The area of the region bounded by θ = π 3 , θ = π 4 , and r = sec θ is:

  1. a) 1 2 ( 3 1 )
  2. b) 3
  3. c) 2 ( 3 1 )
  4. d) 2 3

To determine

To identify: The correct option for the blank in the statement, “The area of the region bounded by the curve r=secθ and θ=π3,θ=π4 is _____”.

Explanation

Given:

The options are, a) 12(31), b) 3, c) 2(31) and d) 23.

Formula used:

The area of the region bounded by the curve r=f(θ) by the rays θ=a and θ=b is given by, A=ab12r2dθ.

Calculation:

The given curve is r=secθ, and θ=π3,θ=π4.

Here, a=π3 and b=π4.

Substitute r=secθ, a=π3 and b=π4 in A=ab12r2dθ,

A=ab12r2dθ=π4π312

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