Indefinite Integrals and Substitution

Indefinite Integrals and Substitution

Assessment

Interactive Video

Mathematics

11th Grade - University

Practice Problem

Hard

CCSS
7.EE.A.1

Standards-aligned

Created by

Amelia Wright

FREE Resource

Standards-aligned

CCSS.7.EE.A.1
The video tutorial explains how to evaluate an indefinite integral using a special type of u substitution. It begins by identifying the need for substitution due to the presence of x both inside and outside a square root. The process involves defining u as the radicand, solving for x, and rewriting the integral in terms of u. The tutorial then covers distributing terms, integrating with respect to u, and simplifying the result. Finally, the antiderivative is expressed in terms of x, providing a complete solution to the integral problem.

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10 questions

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1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the main challenge in evaluating the given indefinite integral?

The need for partial fraction decomposition.

The presence of x both inside and outside the square root.

The presence of a constant factor.

The need for integration by parts.

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the u-substitution process, what is u initially set equal to?

The derivative of x

The square root of x

x + 2

x - 2

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the differential du equal to in terms of dx?

2dx

dx

x dx

0

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How is x expressed in terms of u during the substitution?

x = 2u

x = u + 2

x = u

x = u - 2

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the expression for the square root of u in terms of u?

u^(-1/2)

u^(3/2)

u^(1/2)

u^2

Tags

CCSS.7.EE.A.1

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the result of integrating 6u^(3/2) with respect to u?

6u^(5/2) / (5/2)

6u^(5/2) / (3/2)

6u^(1/2) / (5/2)

6u^(1/2) / (3/2)

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the reciprocal of 5/2 used for in the integration process?

To add to the integrated term

To subtract from the integrated term

To divide the integrated term

To multiply the integrated term

Tags

CCSS.7.EE.A.1

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