Understanding Indefinite Integrals and U-Substitution

Understanding Indefinite Integrals and U-Substitution

Assessment

Interactive Video

Mathematics

9th - 12th Grade

Hard

CCSS
6.EE.A.2B

Standards-aligned

Created by

Mia Campbell

FREE Resource

Standards-aligned

CCSS.6.EE.A.2B
This video tutorial covers the indefinite integration of exponential functions, starting with basic concepts and moving through examples. It explains the integration of functions like 5^x and 3^7x, using a formula involving the derivative of the exponent. The video then tackles a more complex problem using u-substitution, demonstrating how to integrate 4x times 5 raised to the x squared. Finally, a practice problem is provided to reinforce the concepts learned.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the first step in solving the indefinite integral of 4x times 5 raised to the x squared?

Find the derivative of 4x

Identify the base and exponent

Use u-substitution

Apply the power rule

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which formula is used to integrate a constant raised to a variable?

a^u divided by u prime times ln a

a^u times u prime

a^u plus the constant of integration

a^u times ln a

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the example of integrating 3 raised to the 7x, what is the value of u prime?

3

7

21

1

Tags

CCSS.6.EE.A.2B

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the base in the expression 9 raised to the 4x plus 5?

5

4

9

x

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What substitution is made for u in the original problem of 4x times 5 raised to the x squared?

u = 5

u = x squared

u = 4x

u = x

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How do you verify the solution to an indefinite integral?

By checking the constant of integration

By taking the derivative

By solving a similar problem

By integrating again

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the practice problem, what is the derivative of x cubed?

x cubed

3x

x squared

3x squared

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