Calculus: Average Value of a Function

Calculus: Average Value of a Function

Assessment

Interactive Video

Mathematics

11th Grade - University

Hard

Created by

Jackson Turner

FREE Resource

The video tutorial explains how to find the average value of a function over a given interval. It begins by introducing the concept of average value and the integral formula used to calculate it. The function is piecewise-defined, so the integral is split into two parts. The tutorial then demonstrates how to calculate the antiderivatives for each part and evaluate the definite integrals. Finally, the results are simplified to find the average value of the function over the interval.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the formula for finding the average value of a function over an interval?

The product of the function values at the endpoints of the interval

The integral of the function over the interval divided by the length of the interval

The sum of the function values at the endpoints of the interval

The derivative of the function at the midpoint of the interval

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Why is the integral broken into two parts in this problem?

To make the calculation easier

Because the function is piecewise-defined

To avoid complex numbers

To simplify the derivative

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the antiderivative of 1 with respect to x?

x^2

1

x

0

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the antiderivative of e to the negative 4x?

Negative 4e to the negative 4x

e to the negative 4x

4e to the negative 4x

Negative e to the negative 4x divided by 4

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What rule is applied to find the antiderivative of e to the negative 4x?

Power rule

Chain rule

Product rule

Quotient rule

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the value of cosine of 0?

1

0

-1

2

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the final expression for the average value of the function?

3 plus 2 cosine of negative 1 plus e to the negative 4 over 4

13/4 minus 2 cosine of negative 1 minus e to the negative 4 over 4

1/2 times 2 plus cosine of negative 1 plus e to the negative 4 over 4

2 minus cosine of negative 1 minus e to the negative 4 over 4

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