Answer:
Target, Google, and FedEx are ones of many different logos.
Step-by-step explanation:
Answer:
6 because that is where the paarabola crosses the y line
Step-by-step explanation:
It looks like
![y(x)=\displaystyle\int_{\cos x}^{\sin x}(3+v^5)^8\,\mathrm dv](https://tex.z-dn.net/?f=y%28x%29%3D%5Cdisplaystyle%5Cint_%7B%5Ccos%20x%7D%5E%7B%5Csin%20x%7D%283%2Bv%5E5%29%5E8%5C%2C%5Cmathrm%20dv)
(If the limits are in the wrong order, just multiply the result by -1)
Split the integral at an arbitrary value between
![\cos x](https://tex.z-dn.net/?f=%5Ccos%20x)
and
![\sin x](https://tex.z-dn.net/?f=%5Csin%20x)
, and write
![y(x)](https://tex.z-dn.net/?f=y%28x%29)
as
![y(x)=\displaystyle\left\{\int_{\cos x}^c+\int_c^{\sin x}\right\}(3+v^5)^8\,\mathrm dv](https://tex.z-dn.net/?f=y%28x%29%3D%5Cdisplaystyle%5Cleft%5C%7B%5Cint_%7B%5Ccos%20x%7D%5Ec%2B%5Cint_c%5E%7B%5Csin%20x%7D%5Cright%5C%7D%283%2Bv%5E5%29%5E8%5C%2C%5Cmathrm%20dv)
![y(x)=\displaystyle\int_c^{\sin x}(3+v^5)^8\,\mathrm dv-\int_c^{\cos x}(3+v^5)^8\,\mathrm dv](https://tex.z-dn.net/?f=y%28x%29%3D%5Cdisplaystyle%5Cint_c%5E%7B%5Csin%20x%7D%283%2Bv%5E5%29%5E8%5C%2C%5Cmathrm%20dv-%5Cint_c%5E%7B%5Ccos%20x%7D%283%2Bv%5E5%29%5E8%5C%2C%5Cmathrm%20dv)
Then by the FTC,
![\dfrac{\mathrm dy}{\mathrm dx}=(3+\sin^5x)^8\cdot\dfrac{\mathrm d\sin x}{\mathrm dx}-(3+\cos^5x)^8\cdot\dfrac{\mathrm d\cos x}{\mathrm dx}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dx%7D%3D%283%2B%5Csin%5E5x%29%5E8%5Ccdot%5Cdfrac%7B%5Cmathrm%20d%5Csin%20x%7D%7B%5Cmathrm%20dx%7D-%283%2B%5Ccos%5E5x%29%5E8%5Ccdot%5Cdfrac%7B%5Cmathrm%20d%5Ccos%20x%7D%7B%5Cmathrm%20dx%7D)