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Integration Techniques and U Substitution

Integration Techniques and U Substitution

Assessment

Interactive Video

Mathematics

11th Grade - University

Practice Problem

Hard

CCSS
8.EE.A.2, HSF.TF.C.8

Standards-aligned

Created by

Liam Anderson

FREE Resource

Standards-aligned

CCSS.8.EE.A.2
,
CCSS.HSF.TF.C.8
The video tutorial explains how to solve an integral using a formula from a calculus textbook. It involves performing a U substitution where U squared equals X to the fourth and A squared equals 16. The integral is rewritten to match the formula, and differential substitution is used to simplify the expression. The final integration is performed, resulting in a solution involving a natural logarithm and a constant of integration.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the main goal of the integration problem discussed in the video?

To evaluate a definite integral

To solve a differential equation

To find the derivative of a function

To find the integral of X divided by the square root of X to the fourth plus 16

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Where can the integration formula used in the video typically be found?

In a chemistry textbook

In a physics textbook

In the back of a calculus textbook under integration tables

In the front of a calculus textbook

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What initial challenge is mentioned regarding the integration formula?

The formula is not applicable to any function

There is an extra factor of X in the numerator

The formula requires a definite integral

The formula is only for polynomials

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What substitution is suggested to overcome the challenge in the integration?

V substitution

W substitution

U substitution

T substitution

Tags

CCSS.8.EE.A.2

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the U substitution, what does U squared equal?

16

X squared

X to the fourth

X cubed

Tags

CCSS.8.EE.A.2

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the value of A when A squared equals 16?

2

16

8

4

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How is the integral rewritten to match the integration formula?

By multiplying the numerator by a constant

By expressing X to the fourth as X squared squared and 16 as four squared

By using a different variable

By changing the limits of integration

Tags

CCSS.HSF.TF.C.8

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