Yes it's exactly due to symmetry. Specifically, symmetry about the x axis.
Simply writing ![\displaystyle \int_{-8}^{-4}\left[\sqrt{x+8} \ \right]dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint_%7B-8%7D%5E%7B-4%7D%5Cleft%5B%5Csqrt%7Bx%2B8%7D%20%5C%20%5Cright%5Ddx)
, without the 2 out front, will only get you the area of the portion shown in red (see diagram below).
The blue region has equal area of the red region due to symmetry.
So,
![\displaystyle 2\int_{-8}^{-4}\left[\sqrt{x+8} \ \right]dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%202%5Cint_%7B-8%7D%5E%7B-4%7D%5Cleft%5B%5Csqrt%7Bx%2B8%7D%20%5C%20%5Cright%5Ddx)
represents the red and blue regions combined.
The portion in green is ![\displaystyle \int_{-4}^{8}\left[\sqrt{x+8} - \frac{x}{2} \ \right]dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint_%7B-4%7D%5E%7B8%7D%5Cleft%5B%5Csqrt%7Bx%2B8%7D%20-%20%5Cfrac%7Bx%7D%7B2%7D%20%5C%20%5Cright%5Ddx)
which is the integral of the difference of the upper and lower curves over the interval 
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In all honesty, it's probably easier to integrate with respect to y since the given functions are in terms of y initially. Also, there isn't a junction point in which the curves swap places in terms of which one is larger. However, it doesn't hurt to have practice in integrating with respect to x.
If you're curious about what the y integral looks like, then it would be
![\displaystyle \int_{-2}^{4} \bigg[ (2y) - (y^2-8)\bigg] dy](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint_%7B-2%7D%5E%7B4%7D%20%5Cbigg%5B%20%282y%29%20-%20%28y%5E2-8%29%5Cbigg%5D%20dy)
You can use a tool like WolframAlpha to check that both integral expressions result in 36 to help confirm that they represent the same overall area (just in different ways of course).
17.10 is the sale price.
I don’t know how to explain but hope this helps.
Answer:
80 Miles
Step-by-step explanation:
If you convert 15 minutes to hours, you get .25 hours. Then, you use that number and multiply it by 320 to get your answer; 80 miles.
Angle B is the largest angle. , Option D is the correct answer.
<h3>What is an Isosceles Triangle ?</h3>
A triangle that has two sides equal is called an Isosceles Triangle.
It is given in the question a triangle ABC
With BA =BC
therefore angle A is equal to angle C
In a triangle the angle opposite to the longest side is the biggest angle
Therefore angle B is the largest angle.
Option D is the correct answer.
To know more about Isosceles Triangle
brainly.com/question/2456591
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Answer:
Step-by-step explanation:
The original questions is suppose an ant walks counterclockwise on a unit circle from the point (1,0) to the endpoint of the radius that forms an angle of 240 degrees with the positive horizontal axis.
To find the distance ant walked we find the arc length of the sector with central angle 240 degree and radius =1 (unit circle)
arc length of a sector =
arc length of a sector =
arc length of a sector =
