Calculus Concepts and Applications

Calculus Concepts and Applications

Assessment

Interactive Video

Mathematics, Science

10th - 12th Grade

Practice Problem

Hard

Created by

Liam Anderson

FREE Resource

The video tutorial explains how to find the surface area of a surface generated by rotating a curve defined by parametric equations about the x-axis. It introduces the formula used for calculating the surface area of revolution, emphasizing the role of the integrand and the radius. The tutorial demonstrates the application of the formula, including the use of derivatives and the chain rule, and simplifies the integrand for easier integration. Finally, it performs the integration using u-substitution and calculates the surface area, providing a clear and detailed walkthrough of the entire process.

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10 questions

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1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the main goal of the problem discussed in the video?

To find the area under a curve

To find the surface area of a curve

To find the volume of a solid

To find the length of a curve

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

When rotating a curve about the x-axis, which variable represents the radius in the integrand?

y

x

z

t

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the role of the variable y in the integrand when rotating about the x-axis?

It represents the height

It represents the radius

It represents the angle

It represents the arc length

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What mathematical rule is applied to find the derivatives dx/dt and dy/dt?

Chain Rule

Quotient Rule

Power Rule

Product Rule

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the derivative of cosine t used in the calculation of dx/dt?

sine t

-sine t

cosine t

-cosine t

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the greatest common factor factored out from the radicand during simplification?

9

9 cosine squared t

9 sine squared t

9 cosine squared t sine squared t

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the simplified form of the expression under the square root after factoring?

9 sine squared t cosine squared t

3 sine squared t cosine squared t

9 sine t cosine t

3 sine t cosine t

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