Answer: b
sorry cant give explanation
Answer: use search website
Step-by-step explanation: its good
Answer:
Answer is ![\frac{4}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B3%7D)
Step-by-step explanation:
To find the interval of x. Use our equations to equal each other.
![-x^2+2x=y,y=0](https://tex.z-dn.net/?f=-x%5E2%2B2x%3Dy%2Cy%3D0)
![-x^2+2x=0\\-x(x-2)=0\\-x=0 , (x-2)=0\\x=0 ,2](https://tex.z-dn.net/?f=-x%5E2%2B2x%3D0%5C%5C-x%28x-2%29%3D0%5C%5C-x%3D0%20%2C%20%28x-2%29%3D0%5C%5Cx%3D0%20%2C2)
![\int\limits^2_0 {-x^2+2x} \, dx](https://tex.z-dn.net/?f=%5Cint%5Climits%5E2_0%20%7B-x%5E2%2B2x%7D%20%5C%2C%20dx)
Integrate.
![\frac{-x^3}{3}+x^2\\(\frac{-2^3}{3}+2^2)-[\frac{-0^3}{3}+0^2]\\-\frac{8}{3} +4-0\\-\frac{8}{3}+\frac{12}{3} =4/3](https://tex.z-dn.net/?f=%5Cfrac%7B-x%5E3%7D%7B3%7D%2Bx%5E2%5C%5C%28%5Cfrac%7B-2%5E3%7D%7B3%7D%2B2%5E2%29-%5B%5Cfrac%7B-0%5E3%7D%7B3%7D%2B0%5E2%5D%5C%5C-%5Cfrac%7B8%7D%7B3%7D%20%2B4-0%5C%5C-%5Cfrac%7B8%7D%7B3%7D%2B%5Cfrac%7B12%7D%7B3%7D%20%20%3D4%2F3)
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.
Just multiply man 2*4 2*3 1.5*4 and 1.5*3.