Answer: A
Step-by-step explanation:
Answer:

Step-by-step explanation:
The integral of a function gives you the area under the curve, the subtraction of one of the areas from the other will give you the area in between.
The limits of integration are the points where the curves intersect each other(take the curves has a system of equation and solve for x and y):


The integral will be the subtraction of the curve
and
(In the graph you can see y=3x is the upper curve):

<h3>
<u>Correct Question :- </u></h3>


(a) 0
(b) 8000
(c) 8080
(d) 16000

Given that

We know


And


Also, given that


and

Now, Consider





![\sf \: = 20\bigg[ {a}^{2} + {b}^{2} + {c}^{2} + {d}^{2}\bigg]](https://tex.z-dn.net/?f=%20%5Csf%20%5C%3A%20%20%3D%2020%5Cbigg%5B%20%7Ba%7D%5E%7B2%7D%20%2B%20%20%7Bb%7D%5E%7B2%7D%20%2B%20%7Bc%7D%5E%7B2%7D%20%2B%20%20%7Bd%7D%5E%7B2%7D%5Cbigg%5D)
We know,

So, using this, we get
![\sf \: = 20\bigg[ {(a + b)}^{2} - 2ab + {(c + d)}^{2} - 2cd\bigg]](https://tex.z-dn.net/?f=%20%5Csf%20%5C%3A%20%20%3D%2020%5Cbigg%5B%20%7B%28a%20%2B%20b%29%7D%5E%7B2%7D%20-%202ab%20%2B%20%20%7B%28c%20%2B%20d%29%7D%5E%7B2%7D%20-%202cd%5Cbigg%5D)
![\sf \: = 20\bigg[ {( - 20)}^{2} + 2(2020) + {(20)}^{2} - 2(2020)\bigg]](https://tex.z-dn.net/?f=%20%5Csf%20%5C%3A%20%20%3D%2020%5Cbigg%5B%20%7B%28%20-%2020%29%7D%5E%7B2%7D%20%2B%20%202%282020%29%20%2B%20%20%7B%2820%29%7D%5E%7B2%7D%20-%202%282020%29%5Cbigg%5D)
![\sf \: = 20\bigg[ 400 + 400\bigg]](https://tex.z-dn.net/?f=%20%5Csf%20%5C%3A%20%20%3D%2020%5Cbigg%5B%20400%20%2B%20400%5Cbigg%5D)
![\sf \: = 20\bigg[ 800\bigg]](https://tex.z-dn.net/?f=%20%5Csf%20%5C%3A%20%20%3D%2020%5Cbigg%5B%20800%5Cbigg%5D)

Hence,

<em>So, option (d) is correct.</em>