
Understanding Double Integrals and Change of Variables

Interactive Video
•
Mathematics
•
11th Grade - University
•
Hard
Standards-aligned

Aiden Montgomery
FREE Resource
Standards-aligned
Read more
10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the shape of the region defined by the inequality 25x² + 4y² ≤ 100?
Parabola
Ellipse
Rectangle
Circle
Tags
CCSS.HSG.CO.A.2
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What transformation is applied to convert the elliptical region into a circular one?
x = 5u, y = 2v
x = 4u, y = 25v
x = 2u, y = 5v
x = u/2, y = v/5
Tags
CCSS.HSG.CO.A.2
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the purpose of the Jacobian in the change of variables?
To convert the integral into a single variable
To adjust the integrand for the change of variables
To transform the region into a square
To find the limits of integration
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How is the double integral simplified using polar coordinates?
By converting the region into a square
By changing the limits of integration
By introducing a new variable
By using trigonometric identities
Tags
CCSS.HSN.CN.B.4
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What are the limits of integration for r in polar coordinates?
0 to 2π
0 to 10
0 to 5
0 to 1
Tags
CCSS.HSN.CN.B.4
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the antiderivative of 40r³cos²θ with respect to r?
5r⁴cosθ
20r³cosθ
40r²cos²θ
10r⁴cos²θ
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which trigonometric identity is used to simplify the integration of cos²θ?
cos²θ = 1 - sin²θ
cos²θ = 1/2(1 + cos2θ)
cos²θ = sin²θ + cos²θ
cos²θ = 1/2(1 - cos2θ)
Create a free account and access millions of resources
Similar Resources on Wayground
11 questions
How to Simplify Pythagorean Identities | 18 Examples

Interactive video
•
11th Grade - University
11 questions
Integration Techniques and Area Calculation

Interactive video
•
11th Grade - University
11 questions
Polar Curves and Area Calculations

Interactive video
•
11th Grade - University
11 questions
Calculus and Trigonometry Concepts

Interactive video
•
11th Grade - University
10 questions
Understanding Polar Coordinates Concepts

Interactive video
•
11th - 12th Grade
11 questions
Jacobian and Triple Integrals Evaluation

Interactive video
•
10th - 12th Grade
11 questions
Differentiation and Trigonometric Identities

Interactive video
•
11th - 12th Grade
11 questions
Master Verifying an identity using the double angle formulas

Interactive video
•
11th Grade - University
Popular Resources on Wayground
10 questions
Video Games

Quiz
•
6th - 12th Grade
20 questions
Brand Labels

Quiz
•
5th - 12th Grade
15 questions
Core 4 of Customer Service - Student Edition

Quiz
•
6th - 8th Grade
15 questions
What is Bullying?- Bullying Lesson Series 6-12

Lesson
•
11th Grade
25 questions
Multiplication Facts

Quiz
•
5th Grade
15 questions
Subtracting Integers

Quiz
•
7th Grade
22 questions
Adding Integers

Quiz
•
6th Grade
10 questions
Exploring Digital Citizenship Essentials

Interactive video
•
6th - 10th Grade
Discover more resources for Mathematics
20 questions
Parallel lines and transversals

Quiz
•
9th - 12th Grade
9 questions
Geometry and Trigonometry Concepts

Interactive video
•
9th - 12th Grade
31 questions
2.1.3 Angle relationships

Quiz
•
10th - 11th Grade
10 questions
Angle Relationships with Parallel Lines and a Transversal

Quiz
•
9th - 12th Grade
11 questions
Solving Multistep Equations Quiz

Quiz
•
11th Grade
10 questions
Intro to Parallel and Perpendicular Slopes

Quiz
•
9th - 12th Grade
15 questions
Absolute Value Equations and Inequalities

Quiz
•
9th - 11th Grade
15 questions
Intro To Compound Inequalities

Quiz
•
9th - 12th Grade