please can I have step by step and formula with an explanation **Problem: Surface Area of Revolution**Find the exact area of the surface obtained by rotating the curve about the x-axis.**Function:**\[ y = \sqrt{5 - x} \]for the interval \[ 3 \leq x \leq 5 \]**Graph Description:**The graph displays the curve \( y = \sqrt{5 - x} \) within the specified domain. The curve is plotted on a Cartesian plane with the x-axis ranging from approximately -1 to 6 and the y-axis ranging from -2 to 2. - The curve starts at the point (3, 1.414) since \( y = \sqrt{5 - 3} = \sqrt{2} \).- It ends at the point (5, 0), where \( y = \sqrt{5 - 5} = 0 \).- The curve represents a downward slope, concave downward as it approaches the x-axis at x = 5.The task is to determine the surface area generated when this segment of the curve is revolved around the x-axis.

Given:- y=√(5-x) , [3, 5] To find:- Area of surface rotating about x axisHence Exact surface area of rotation about x axis is 13π/3 square units

Answered: Find the exact area of the surface…

Math

Calculus

Find the exact area of the surface obtained by rotating the curve about the x-axis y = v5 – x, 3

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

please can I have step by step and formula with an explanation

**Problem: Surface Area of Revolution**

Find the exact area of the surface obtained by rotating the curve about the x-axis.

**Function:**
\[ y = \sqrt{5 - x} \]
for the interval \[ 3 \leq x \leq 5 \]

**Graph Description:**

The graph displays the curve \( y = \sqrt{5 - x} \) within the specified domain. The curve is plotted on a Cartesian plane with the x-axis ranging from approximately -1 to 6 and the y-axis ranging from -2 to 2.

- The curve starts at the point (3, 1.414) since \( y = \sqrt{5 - 3} = \sqrt{2} \).
- It ends at the point (5, 0), where \( y = \sqrt{5 - 5} = 0 \).
- The curve represents a downward slope, concave downward as it approaches the x-axis at x = 5.

The task is to determine the surface area generated when this segment of the curve is revolved around the x-axis.

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