Definite Integrals and Functions

Definite Integrals and Functions

Assessment

Interactive Video

Mathematics

9th - 12th Grade

Hard

Created by

Lucas Foster

FREE Resource

The video tutorial explains how to determine the value of a definite integral involving three functions: F(x), G(x), and H(x). It introduces the problem, highlighting that the upper and lower limits of integration are the same for all given integrals. The tutorial then explains two key properties of definite integrals: factoring out constants and breaking up integrals of sums or differences. These properties are applied to solve the given integral, resulting in a final value of -14. The tutorial concludes with a summary of the calculations and the final result.

Read more

10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the main task in the given problem involving definite integrals?

To find the indefinite integral of a function.

To solve a system of linear equations.

To determine the value of a definite integral involving multiple functions.

To differentiate a function with respect to x.

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which property allows you to factor out a constant from a definite integral?

The sum property of integrals.

The constant multiple property of integrals.

The chain rule of differentiation.

The product rule of differentiation.

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How can you handle the integral of a sum or difference of functions?

By integrating each function separately and then adding or subtracting the results.

By multiplying the integrals of the functions.

By differentiating each function separately.

By finding the average of the integrals.

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the first step in breaking down the integral of -3xF(x) + 2xG(x) - H(x)?

Multiply the integrals together.

Factor out the constants -3 and 2 from the integrals.

Differentiate each function.

Integrate each function separately without factoring.

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the value of the integral of F(x) from 2 to 14?

8

28

14

39

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the value of the integral of G(x) from 2 to 14?

39

8

28

14

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the value of the integral of H(x) from 2 to 14?

28

8

14

39

Create a free account and access millions of resources

Create resources
Host any resource
Get auto-graded reports
or continue with
Microsoft
Apple
Others
By signing up, you agree to our Terms of Service & Privacy Policy
Already have an account?