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Physics and Calculus Concepts Assessment

Physics and Calculus Concepts Assessment

Assessment

Interactive Video

Mathematics

9th - 12th Grade

Hard

Created by

Thomas White

FREE Resource

The video tutorial covers solving differential equations with initial conditions using integration techniques such as u-substitution and integration by parts. It explains how to derive the original equation from a differential equation and solve for constants using initial conditions. The tutorial also includes examples of finding the position function of a moving particle and modeling the height of a dropped ball using differential equations.

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22 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the first step in solving the differential equation dy/dx = x√(x² + 9)?

Differentiate both sides

Use integration by parts

Integrate both sides

Apply the initial condition

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which substitution is used to solve the integral of x√(x² + 9) dx?

u = x

u = x² + 9

u = √(x² + 9)

u = x√(x² + 9)

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

After substituting u = x² + 9, what is the expression for du?

du = 2x dx

du = x dx

du = dx

du = 3x dx

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the value of the constant of integration c if y(-4) = 0?

c = 1/3

c = -125/3

c = 125/3

c = 0

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the final solution for y in terms of x for the given differential equation?

y = 1/3 (x² + 9)^(3/2) + 125/3

y = 1/3 (x² + 9)^(3/2) - 125/3

y = 1/2 (x² + 9)^(3/2) - 125/3

y = 1/3 (x² + 9)^(3/2)

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What technique is used to solve the integral of x e^(-x) dx?

Integration by parts

U-substitution

Partial fraction decomposition

Trigonometric substitution

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In integration by parts, what is chosen as u for the integral of x e^(-x) dx?

u = e^(-x)

u = x

u = x e^(-x)

u = 1

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