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Integration Techniques and Common Mistakes

Integration Techniques and Common Mistakes

Assessment

Interactive Video

Mathematics

9th - 10th Grade

Practice Problem

Hard

Created by

Emma Peterson

FREE Resource

The video tutorial covers indefinite integrals, highlighting common student errors in integration and differentiation. A mnemonic device is introduced to help remember the rules: integrals increase powers, while derivatives decrease them. The tutorial includes exercises with simple examples, negative indices, fractions, and expanding brackets, providing step-by-step solutions to enhance understanding and fluency in integration.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is a common mistake students make when dealing with powers in calculus?

Using the wrong variable

Forgetting to add constants

Confusing integration with differentiation

Ignoring negative signs

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What mnemonic device helps remember the rule for integrals?

Derivatives increase powers

Integrals decrease powers

Integrals increase powers

Derivatives remain constant

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

When integrating x^n, what is the new power of x?

n

n-1

2n

n+1

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the integral of x^4 - x^3?

x^5 - x^4 + C

x^5/5 - x^4/4 + C

x^4/4 - x^3/3 + C

x^5/5 + x^4/4 + C

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How do you handle negative indices when integrating?

Increase the index by one

Convert them to positive indices

Ignore them

Decrease the index by one

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the integral of x^-8?

x^-7/7 + C

-x^-7/7 + C

x^-9/9 + C

-x^-9/9 + C

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

When integrating fractions, what should you be careful about?

Adding fractions directly

Ignoring the denominator

Increasing the index by one

Using common denominators

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