Calculate the surface area of the object obtained by rotating the following shaded area around x-axis:

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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**Title**: Calculating Surface Area of a Rotated Object

**Problem Statement**: Calculate the surface area of the object obtained by rotating the following shaded area around the x-axis.

**Graph Description**:
- The graph consists of a right-angled triangle in the coordinate plane.
- The triangle's base extends from x = -1 to x = 1 on the x-axis.
- The height of the triangle reaches y = 1 on the y-axis.
- The shaded area is the interior of this triangle.

**Explanation**:
The shaded triangle will be rotated around the x-axis to generate a three-dimensional object, specifically a cone. To find the surface area of this cone, calculus methods like surface area integrals can be applied. Note that the generated surface area will include only the lateral surface of the cone and not the bases.
Transcribed Image Text:**Title**: Calculating Surface Area of a Rotated Object **Problem Statement**: Calculate the surface area of the object obtained by rotating the following shaded area around the x-axis. **Graph Description**: - The graph consists of a right-angled triangle in the coordinate plane. - The triangle's base extends from x = -1 to x = 1 on the x-axis. - The height of the triangle reaches y = 1 on the y-axis. - The shaded area is the interior of this triangle. **Explanation**: The shaded triangle will be rotated around the x-axis to generate a three-dimensional object, specifically a cone. To find the surface area of this cone, calculus methods like surface area integrals can be applied. Note that the generated surface area will include only the lateral surface of the cone and not the bases.
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