Answer:
12
Step-by-step explanation:
Answer:
f(x) = -2x² - 8x - 2
General Formulas and Concepts:
- Order of Operations: BPEMDAS
- Expand by FOIL (First Outside Inside Last)
- Standard Form: f(x) = ax² + bx + c
- Vertex Form: f(x) = a(bx + c)² + d
Step-by-step explanation:
<u>Step 1: Define function</u>
Vertex Form: f(x) = -2(x + 2)² + 6
<u>Step 2: Find Standard Form</u>
- Expand by FOILing: f(x) = -2(x² + 4x + 4) + 6
- Distribute -2: f(x) = -2x² - 8x - 8 + 6
- Combine like terms (constants): f(x) = -2x² - 8x - 2
One way to capture the domain of integration is with the set

Then we can write the double integral as the iterated integral

Compute the integral with respect to
.

Compute the remaining integral.

We could also swap the order of integration variables by writing

and

and this would have led to the same result.


TeX rendering has been iffy at best on this site for the past few days, at least in my experience. I've attached a solution below.
To find the slope of the expression:

We need to remember that this is the Slope-intercept Form of the line equation:

Where
m = slope
b is the y-intercept.
Therefore, the slope of the line equation above is m = 3.