Question

I don't understand this question at all please help if you do

Answer 1

Answer is
`(4)/(3)`

Explanation:

To find the interval of x. Use our equations to equal each other.

`-x^2+2x=y,y=0`

`-x^2+2x=0\\-x(x-2)=0\\-x=0 , (x-2)=0\\x=0 ,2`

`\int\limits^2_0 {-x^2+2x} \, dx`

Integrate.

`(-x^3)/(3)+x^2\\((-2^3)/(3)+2^2)-[(-0^3)/(3)+0^2]\\-(8)/(3) +4-0\\-(8)/(3)+(12)/(3) =4/3`

Using Desmos I have Graphs of both of the equations you have provided. The problem asks us to find the shaded region between those curves/equations.

Proof Check your interval of x.