Percentage
A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.
Algebraic Expressions
In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.
Numbers
Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.
Subtraction
Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.
Addition
Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.
![### Step 2: Solution to Problem 6, Homework 5.3
We know that the average value of a function \( f(x) \) over the interval \([a, b]\) is given by:
\[
f_{\text{avg}} = \frac{1}{b-a} \int_{a}^{b} f(x) \, dx
\]
Given:
\[
f(x) = -4x^2 - 4
\]
And the interval \([a, b] = [0, 2]\).
Thus:
\[
f_{\text{avg}} = \frac{1}{2-0} \int_{0}^{2} (-4x^2 - 4) \, dx
\]
\[
= \frac{1}{2} \left[ \frac{-4x^3}{3} - 4x \right]_{0}^{2}
\]
When evaluated, this becomes:
\[
= \frac{1}{2} \left[ \frac{-4 \times 8}{3} - 8 \right]
\]
\[
= \frac{1}{2} \left[ \frac{-32}{3} - 8 \right]
\]
\[
= \frac{1}{2} \left[ \frac{-56}{3} \right]
\]
So, the average value is:
\[
= \frac{-28}{3}
\]
**Note:** There is a note in the margin asking for clarification: "Please explain how the \( x \) is added to the \(-4\)."](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fea9cc4aa-6448-4354-8c80-3956c9525a82%2Fbd0c1534-1527-45e6-a9fd-340ba775d76a%2Fvwh1vm_processed.jpeg&w=3840&q=75)
there we use integral property
i.e.
here integral when nothing is given we take 1 and integrate with respect to x.
if we have
detailed solution is given below
Step by step
Solved in 3 steps with 2 images
