Answer:
7.80
Step-by-step explanation:
46.80 divided by 6 is 7.80
Integration by parts will help here. Letting
![u=\arctan x](https://tex.z-dn.net/?f=u%3D%5Carctan%20x)
and
![\mathrm dv=\mathrm dx](https://tex.z-dn.net/?f=%5Cmathrm%20dv%3D%5Cmathrm%20dx)
, you end up with
![\mathrm du=\dfrac{\mathrm dx}{1+x^2}](https://tex.z-dn.net/?f=%5Cmathrm%20du%3D%5Cdfrac%7B%5Cmathrm%20dx%7D%7B1%2Bx%5E2%7D)
and
![v=x](https://tex.z-dn.net/?f=v%3Dx)
. Now
![\displaystyle\int\arctan x\,\mathrm dx=uv-\int v\,\mathrm du](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint%5Carctan%20x%5C%2C%5Cmathrm%20dx%3Duv-%5Cint%20v%5C%2C%5Cmathrm%20du)
![\displaystyle\int\arctan x\,\mathrm dx=x\arctan x-\int\frac x{1+x^2}\,\mathrm dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint%5Carctan%20x%5C%2C%5Cmathrm%20dx%3Dx%5Carctan%20x-%5Cint%5Cfrac%20x%7B1%2Bx%5E2%7D%5C%2C%5Cmathrm%20dx)
For the remaining integral, setting
![y=1+x^2](https://tex.z-dn.net/?f=y%3D1%2Bx%5E2)
gives
![\dfrac{\mathrm dy}2=x\,\mathrm dx](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20dy%7D2%3Dx%5C%2C%5Cmathrm%20dx)
, so
![\displaystyle\int\frac x{1+x^2}\,\mathrm dx=\frac12\int\frac{\mathrm dy}y=\frac12\ln|y|+C=\frac12\ln(1+x^2)+C](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint%5Cfrac%20x%7B1%2Bx%5E2%7D%5C%2C%5Cmathrm%20dx%3D%5Cfrac12%5Cint%5Cfrac%7B%5Cmathrm%20dy%7Dy%3D%5Cfrac12%5Cln%7Cy%7C%2BC%3D%5Cfrac12%5Cln%281%2Bx%5E2%29%2BC)
Putting everything together, you end up with
Answer:
x^2 +3
Step-by-step explanation:
f(x) = 2x^2 + 2
g(x) = x2 – 1,
find (f – g)(X).
f(x) - g(x) = 2x^2 + 2 -( x^2 – 1)
Distribute the minus sign
= 2x^2 +2 -x^2 +1
= x^2 +3
Both the red and blue line segments stretch from the center of the circle to a point on the circle The length of the blue line segment is 17 How long is the red line segment?
17