Integration Techniques and Concepts

Integration Techniques and Concepts

Assessment

Interactive Video

Mathematics

11th - 12th Grade

Hard

Created by

Sophia Harris

FREE Resource

The video tutorial covers the method of integration by parts, starting with the selection of u and dv, and explaining why x is often chosen as u. It demonstrates the integration process with examples, including differentiating and integrating functions like x e^x. The tutorial also explores more complex scenarios and techniques, emphasizing the importance of understanding the process and recognizing patterns in integration problems.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Why is x often chosen as u in integration by parts?

Because it is always the first term

Because it simplifies to 1 when differentiated

Because it is a constant

Because it is easy to integrate

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the first step in applying the integration by parts formula?

Reading down the column for uv

Subtracting the integral of vdu

Differentiating dv

Integrating u

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the example discussed, what is the integral of x e^x?

x e^x - x

x e^x + e^x

x e^x - e^x

x e^x + x

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the purpose of reading down the left-hand column in integration by parts?

To identify the integral

To determine uv

To check for errors

To find the derivative

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the benefit of solving integration problems without a grid?

It requires less writing

It is more accurate

It helps visualize the process

It is faster

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

When selecting u as x squared, what is the derivative du/dx?

2x

x^2

x

1

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the result of integrating x squared e^x using integration by parts?

x^2 e^x + 2e^x

x^2 e^x - 2e^x

x^2 e^x + 2x e^x

x^2 e^x - 2x e^x

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