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

5 0

3 years ago

A bakery charges two different prices for desserts. The table shows the number of cupcakes and the number of cookies sold in the

andreev551 [17]

Answer:

hope this helps

Step-by-step explanation:do not need one really

8 0

3 years ago

9 of 1

Ghella [55]

X=10 is the answer to this

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3 years ago

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Mary's 3 hamsters each eat three-eighths of cup of grain a day, if she has 6 and 3/4 cups of grain, how many days will the grain

muminat

Hello!

3/8 times 3 equals 9/8 which is also 1 1/8. If you multiply 3/4 by two (numerator and denominator) then you will get 6/8. And if you multiply 9/8( I just find it easier with 9/8) by 6 you will get 54/8. And the grain will last for 6.75 days.

I may be wrong let me know.
Hope this helps!

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3 years ago

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