![\int_{0}^{1}\frac{1}{1+x^2}dx](https://tex.z-dn.net/?f=%5Cint_%7B0%7D%5E%7B1%7D%5Cfrac%7B1%7D%7B1%2Bx%5E2%7Ddx)
The integral above is definite so we must first calculate for indefinite one.
![\int{\frac{1}{1+x^2}dx}](https://tex.z-dn.net/?f=%5Cint%7B%5Cfrac%7B1%7D%7B1%2Bx%5E2%7Ddx%7D)
Rule:
![\int{\frac{1}{a^2+b^2}dx}=\frac{1}{b}\times\arctan(\frac{a}{b})](https://tex.z-dn.net/?f=%5Cint%7B%5Cfrac%7B1%7D%7Ba%5E2%2Bb%5E2%7Ddx%7D%3D%5Cfrac%7B1%7D%7Bb%7D%5Ctimes%5Carctan%28%5Cfrac%7Ba%7D%7Bb%7D%29)
.
Now we apply this rule and get:
![\int{\frac{1}{1+x^2}}=\frac{1}{1}\times\arctan(\frac{x}{1})](https://tex.z-dn.net/?f=%5Cint%7B%5Cfrac%7B1%7D%7B1%2Bx%5E2%7D%7D%3D%5Cfrac%7B1%7D%7B1%7D%5Ctimes%5Carctan%28%5Cfrac%7Bx%7D%7B1%7D%29)
Or just simply:
![\arctan(x)](https://tex.z-dn.net/?f=%5Carctan%28x%29)
Now we integrate:
![\arctan(x)\Big\vert_{0}^{1}](https://tex.z-dn.net/?f=%5Carctan%28x%29%5CBig%5Cvert_%7B0%7D%5E%7B1%7D)
![\arctan(1)-\arctan(0)](https://tex.z-dn.net/?f=%5Carctan%281%29-%5Carctan%280%29)
Answer:
C
Step-by-step explanation:
Tides can be predicted far in advance and with a high degree of accuracy. Tides are forced by the orbital relationships between the Earth, the moon and the Sun. ... The predictability of planetary motion means that we can also reconstruct tides in the past.
Answer:
Here you go!
Step-by-step explanation:
Do tell if it still seems difficult.
:)