
Calculus: Integrals and Derivatives
Interactive Video
•
Mathematics
•
11th Grade - University
•
Practice Problem
•
Hard
Liam Anderson
FREE Resource
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the equation of the plane over which the surface integral is evaluated?
z = 4 + x + 3y
z = 3 + x + 4y
z = 2 + x + 2y
z = 5 + x + y
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the region R in the xy-plane for the given surface integral problem?
A circle with radius 2
A rectangle with x from 0 to 2 and y from 0 to 3
A triangle with vertices at (0,0), (2,0), and (0,3)
A square with side length 3
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the surface integral formula, what does the term under the square root represent?
The magnitude of the normal vector to the surface
The area of the region R
The gradient of the function g(x, y)
The volume under the surface
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the partial derivative of g(x, y) = 4 + x + 3y with respect to x?
4
0
1
3
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the partial derivative of g(x, y) = 4 + x + 3y with respect to y?
0
1
4
3
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the integrand function after substituting g(x, y) for z in the surface integral?
x^2
4x^2 + x^3 + 3x^2y
x^3 + 3x^2y
4x^2 + 3x^2y
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the result of integrating 4x^2 with respect to x from 0 to 2?
4
32/3
8
16/3
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