Shell Method HW

Shell Method HW

Assessment

Flashcard

Mathematics

12th Grade

Practice Problem

Hard

Created by

Wayground Content

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the Shell Method in calculus?

Back

The Shell Method is a technique for finding the volume of a solid of revolution. It involves integrating the lateral surface area of cylindrical shells formed by revolving a region around an axis.

2.

FLASHCARD QUESTION

Front

How do you set up the integral for the Shell Method when revolving around the y-axis?

Back

To set up the integral for the Shell Method when revolving around the y-axis, use the formula: \( V = 2\pi \int_{a}^{b} (radius)(height) \, dx \), where 'radius' is the distance from the y-axis and 'height' is the function value.

3.

FLASHCARD QUESTION

Front

What is the formula for the volume of a solid of revolution using the Shell Method?

Back

The volume \( V \) is given by: \( V = 2\pi \int_{a}^{b} (radius)(height) \, dx \) for rotation around the y-axis, and \( V = 2\pi \int_{c}^{d} (radius)(height) \, dy \) for rotation around the x-axis.

4.

FLASHCARD QUESTION

Front

What is the radius in the Shell Method when revolving around the y-axis?

Back

The radius is the distance from the axis of rotation (y-axis) to the shell, which is typically the x-coordinate of the function being revolved.

5.

FLASHCARD QUESTION

Front

What is the height in the Shell Method when revolving around the y-axis?

Back

The height is the value of the function being revolved, which represents the vertical distance of the shell.

6.

FLASHCARD QUESTION

Front

How do you find the volume of the solid generated by revolving the region bounded by \( y = 2\sqrt{x} \) about the y-axis?

Back

Set up the integral using the Shell Method: \( V = 2\pi \int_{0}^{4} (x)(2\sqrt{x}) \, dx \) and evaluate.

7.

FLASHCARD QUESTION

Front

What is the significance of the limits of integration in the Shell Method?

Back

The limits of integration define the interval over which the region is being revolved, determining the bounds of the volume calculation.

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