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Dmitrij [34]
3 years ago
10

Evaluate the integral by interpreting it in terms of areas Draw a picture of the region the integral

Mathematics
1 answer:
denis23 [38]3 years ago
5 0

Answer:

Step-by-step explanation:

The picture is below of how to separate this into 2 different regions, which you have to because it's not continuous over the whole function. It "breaks" at x = 2. So the way to separate this is to take the integral from x = 0 to x = 2 and then add it to the integral for x = 2 to x = 3. In order to integrate each one of those "parts" of that absolute value function we have to determine the equation for each line that makes up that part.

For the integral from [0, 2], the equation of the line is -3x + 6;

For the integral from [2, 3], the equation of the line is 3x - 6.

We integrate then:

\int\limits^2_0 {-3x+6} \, dx+\int\limits^3_2 {3x-6} \, dx    and

-\frac{3x^2}{2}+6x\left \} {{2} \atop {0}} \right.  +\frac{3x^2}{2}-6x\left \} {{3} \atop {2}} \right.  sorry for the odd representation; that's as good as it gets here!

Using the First Fundamental Theorem of Calculus, we get:

(6 - 0) + (-4.5 - (-6)) = 6 + 1.5 = 7.5

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koban [17]

Answer:

2^{-1}

Explanation:

05/10

Simplifying

1/2

or 2^-1

Hope this helps you. Do mark me as brainlist

4 0
2 years ago
Identify the restrictions on the domain of f(x) = x+2/x-3<br> x≠-2<br> x≠2<br> x≠-3<br> x≠3
erma4kov [3.2K]

Answer:

  x ≠ 3

Step-by-step explanation:

The denominator of ...

  f(x) = (x+2)/(x -3)

is zero when x=3, so the function is not defined there. Values of x for which the function is not defined are not part of the domain.

The restriction is: x ≠ 3.

_____

Please note that parentheses are required around numerators and denominators when a rational function is written in plain text. When it is typeset:

  f(x)=\dfrac{x+2}{x-3}

the division bar serves as a grouping symbol. In plain text, we cannot tell where numerator and denominator begin and end unless some other grouping symbol (parentheses) is used.

4 0
3 years ago
What is x² + 11x + 28​
quester [9]
(X+7)(x+4). 7 times 4 equals 28 while also equaling 11 when added. You use the Foil Method to check you answer (First, Outer, Inner, Last).
7 0
3 years ago
Read 2 more answers
Write the equation of a line in slope intercept form that is parallel to the line y= 1/3x + 5 and passes through (-9, 5)
vladimir2022 [97]
Find the slope of line 1
The equation of line 1 is y = (1/3)x + 5
m = 1/3

Find the slope of line 2
Line 2 is parallel to line 1. Parallel lines have the same number of slope. So the slope of line 2 is 1/3

Find the slope-intercept form of equation, with m = 1/3 and (-9,5)
General formula
y - y₁ = m(x - x₁)

Input the number to the formula
y - y₁ = m(x - x₁)
y - 5 = 1/3(x - (-9))
y - 5 = 1/3 (x + 9)
y - 5 = (1/3)x + 3
y = (1/3)x + 3 + 5
y = (1/3)x + 8

The equation is y = (1/3)x + 8
7 0
3 years ago
2. If mZ1 = 71 degrees, find the measure of the other 7 angles.<br>​
Kobotan [32]
The measure of angles 1,4,5,8 are congruent meaning they’re the exact same. If angle 1 measures 71 degrees then that means that 4,5,8 also measure 71 degrees. Angles 1&2 are supplementary angles which means their sum is 180. Since we know that angle 1 measures 71 then we can find the measure of angle 2 by 71+x=180 and solve for x (angle 2) which is 109
Angles 2,3,6,7 are congruent which means they also equal 109
*** angles 1,4,5,8 = 71
Angles 2,3,6,7 = 109***
3 0
3 years ago
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