Parametrization and Line Integrals

Parametrization and Line Integrals

Assessment

Interactive Video

Mathematics

11th Grade - University

Practice Problem

Hard

CCSS
HSF.TF.A.2, HSG.GPE.A.1

Standards-aligned

Created by

Jackson Turner

FREE Resource

Standards-aligned

CCSS.HSF.TF.A.2
,
CCSS.HSG.GPE.A.1
This video tutorial introduces line integrals in R2, extending concepts from Calculus 1. It explains how to integrate a function along a curve in the XY plane, using parametrization and arc length. The tutorial includes two examples: one along a line segment and another along a circular path in the first quadrant. The video concludes with a summary and a preview of line integrals in R3.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the primary extension of line integrals in R2 compared to Calculus 1?

Calculating the volume under a curve

Integrating a surface along a curve in the XY plane

Finding the slope of a tangent line

Integrating along the x-axis only

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How is the function f(x, y) rewritten in terms of the parameter T?

By replacing x with y and vice versa

By using the components of the vector-valued function R(T)

By integrating over the x-axis

By differentiating with respect to y

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the first step in evaluating a line integral along a curve?

Finding the derivative of the function

Calculating the area under the curve

Parametrizing the path in the XY plane

Differentiating the function with respect to x

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the first example, what is the parametrization of the line segment from (0,0) to (2,4)?

R(T) = (2T, T)

R(T) = (2, 4)

R(T) = (T^2, 2T^2)

R(T) = (T, 2T)

Tags

CCSS.HSF.TF.A.2

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What does the result of the line integral represent in the first example?

The volume under the surface

The area of a fence along the curve

The length of the curve

The slope of the line

Tags

CCSS.HSG.GPE.A.1

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the second example, what is the equation of the circle used for parametrization?

x^2 + y^2 = 8

x^2 + y^2 = 2

x^2 + y^2 = 4

x^2 + y^2 = 1

Tags

CCSS.HSF.TF.A.2

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What trigonometric functions are used to parametrize the circle in the second example?

Sine and cosine

Tangent and cotangent

Exponential and logarithmic

Secant and cosecant

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