Evaluate this integral. I'm not sure how to evaluate integrals with absolute values.

Mathematics

1 answer:

SOVA2 [1]3 years ago

6 0

Answer:

Step-by-step explanation:

The first step is to understand what the integrand looks like. (See the graph below.)

It is -1 for x < 0 and +1 for x > 0. Thus, the value of this integral is ...

$\int\limits^0_{-1} {-1} \, dx + \int\limits^2_0 {1} \, dx=-1+2=1$

_____

Essentially, you treat the absolute value as a piecewise linear function. This is the same way you treat an absolute value in any equation or inequality.

Here, this means you divide the integral into two parts: one where the integrand is -x/x, and one where it is +x/x.

You might be interested in

Evaluate the function.<br><img src="https://tex.z-dn.net/?f=f%28x%29%20%3D%20%20-%20x%5E%7B2%7D%20%20-%207x%20-%205" id="TexForm

Nat2105 [25]

<h3>Answer: 5</h3>

===================================================

Explanation:

Everywhere you see an x, replace it with -5. Then use the order of operations PEMDAS to simplify

$f(x) = -x^2 - 7x - 5\\\\f(-5) = -(-5)^2 - 7(-5) - 5\\\\f(-5) = -(25) - 7(-5) - 5\\\\f(-5) = -25 + 35 - 5\\\\f(-5) = 10 - 5\\\\f(-5) = 5\\\\$

Keep in mind that for the x^2 term, you are squaring all of x = -5, which includes the negative as well. So that means

x^2 = (-5)^2 = (-5)*(-5) = 25

but sticking a negative out front makes

-x^2 = -(-5)^2 = -25

6 0

3 years ago

What are the exact values of x and y?<br><br> x = <br> y =

Mice21 [21]

Answer:

see the attachment photo!

7 0

2 years ago

A population of 5000 people doubles in size every 10 years. Determine the population

Marrrta [24]

Answer: A quantity grows exponentially when its increase is proportional to what is already there. A common example is compound interest, where $100 invested at 7% per year annual compound interest will double in 10 years. Similarly, if a population grows at 7% per year, it, too, will double in 10 years.

Step-by-step explanation:

3 0

3 years ago

A school survey found that 24 out of 30 students prefer chocolate milk to white milk. If the school has 500 students, which is t

Georgia [21]

Answer:

Around 401 students would prefer chocolate milk.

Step-by-step explanation:

500/30=16.66667...

24*16.7=400.8

you cant have an eighth of a vote so you round to 401

4 0