Q20P In Problems 17 to 30, for the cu... [FREE SOLUTION]

Chapter 5: Q20P (page 257)

In Problems 17 to 30, for the curve $y = \sqrt{x}$ , between $x = 0$ and $x = 2$ ,
find:
The curved area of this solid.

Short Answer

Expert verified

The curved area of the solid is $\frac{13 蟺}{3}$

Step by step solution

Definition of double integral

Double integral of $f (x, y)$ over the area, A in the $(x, y)$ plane as the limit of this sum, and it is written as $鈭� {鈭�}_{A} f (x, y) d x d y$

Representation of the area bounded by the curve

Draw the bounded region for the curve $y = \sqrt{x}$ , between $x = 0$ and $x = 2$ .

Determination of the surface element of the solid generated when the area is revolved about the x-axis.

Determine the surface element from the figure.

$d S = 2 蟺蹿 (x) dL = 2 蟺蹿 (x) \sqrt{1 + {(f' (x))}^{2}} dx = 2 蟺 \sqrt{x} \sqrt{1 + \frac{1}{4 x}} dx = 2 蟺 \sqrt{x + \frac{1}{4}} dx$

Step 4: Determination of the total surface of the solid generated when the area is revolved about the axis.

Determine the total surface of the solid generated.

$S = 2 蟺 {鈭�}_{0}^{2} \sqrt{x + \frac{1}{4}} d (x + \frac{1}{4}) {= \frac{4 蟺}{3} {(x + \frac{1}{4})}^{3 / 2}}_{0}^{2} = \frac{13 蟺}{3}$

Thus, the value of curved area of the solid is $\frac{13 蟺}{3}$ .

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91影视

In Problems 17 to 30, for the curve $y = \sqrt{x}$ , between $x = 0$ and $x = 2$ ,
find:
The curved area of this solid.

Short Answer

Step by step solution

Definition of double integral

Representation of the area bounded by the curve

Determination of the surface element of the solid generated when the area is revolved about the x-axis.

Step 4: Determination of the total surface of the solid generated when the area is revolved about the axis.

One App. One Place for Learning.

Most popular questions from this chapter

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91影视

In Problems 17 to 30, for the curve y=x, betweenx=0and x=2,find:The curved area of this solid.

Short Answer

Step by step solution

Definition of double integral

Representation of the area bounded by the curve

Determination of the surface element of the solid generated when the area is revolved about the x-axis.

Step 4: Determination of the total surface of the solid generated when the area is revolved about the axis.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Solid State Physics

Turning Points in Physics

Fields in Physics

Electrostatics

Space Physics

Electricity and Magnetism

Study anywhere. Anytime. Across all devices.

In Problems 17 to 30, for the curve $y = \sqrt{x}$ , between $x = 0$ and $x = 2$ ,
find:
The curved area of this solid.