Q. 13 Set up and solve definite integr... [FREE SOLUTION]

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Chapter 6: Q. 13 (page 574)

Set up and solve definite integrals to find each volume, surface area, or arc length that follows. Solve each volume problem both with disks/washers and with shells, if possible .
The area of the surface obtained by revolving the curve $f (x) = \sin (蟺虫)$ around the $x$ -axis on $[鈭� 1, 1]$ .

Short Answer

Expert verified

The area of the surface obtained by revolving the curve $f (x) = \sin (蟺虫)$ around the $x$ -axis on $[- 1, 1]$ .

Step by step solution

Step 1. Given Information.

The area of the surface obtained by revolving the curve $f (x) = \sin (蟺虫)$ around the $x$ -axis on $[- 1, 1]$ .

Step 2. Formulation.

Let $f (x)$ be a nonnegative smooth function over the interval $[a, b]$ . Then, the surface area of the surface of revolution formed by revolving the graph of $f (x)$ around the $x$ -axis .

The surface area of the curve is given by

localid="1652678755610" $S = 2 蟺 {鈭�}_{a}^{b} f (x) \sqrt{(f' {(x))}^{2} + 1} d x$ .

Step 3. Calculation.

$f (x) = \sin (蟺虫) f' (x) = 蟺肠辞蝉 (蟺虫)$

Then, the function will be

role="math" localid="1652679014405" $S = 2 蟺 {鈭�}_{- 1}^{1} \sin (蟺虫) \sqrt{{(蟺肠辞蝉 (蟺虫))}^{2} + 1} d x S = 2 蟺 {鈭�}_{- 1}^{1} \sin (蟺虫) \sqrt{(蟺^{2} \cos^{2} (蟺虫)) + 1} d x L e t \cos (蟺虫) = t 鈬� - 蟺蝉颈苍 (蟺虫) dx = dt If x = - 1, t = - 1 x = 1, t = - 1 S = - {鈭�}_{- 1}^{- 1} \sqrt{(蟺^{2} t^{2}) + 1} dt S = 0$

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Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Formulation.

Step 3. Calculation.

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91影视

Set up and solve definite integrals to find each volume, surface area, or arc length that follows. Solve each volume problem both with disks/washers and with shells, if possible .The area of the surface obtained by revolving the curve f(x)=sin蟺虫around the x-axis on [鈭�1,1].

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Formulation.

Step 3. Calculation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Geometry

Logic and Functions

Calculus

Mechanics Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.