![\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)
You start by adding 1073 and 1108 together to get 2181 then subtract 2181 from the 3 thousand to get 819. the restaurant needs to earn 819 dollars (as a minimum) on Sunday.
Answer:
Arc length s = 15.3 inches
Step-by-step explanation:
We know that length of an arc that subtends an angle θ radians at the center is given by
![s=r\times \Theta](https://tex.z-dn.net/?f=s%3Dr%5Ctimes%20%5CTheta)
where
r is the radius of the circle
θ is the angle subtended in radians
Thus applying values we get ![s=3.4\times \ 4.5radians](https://tex.z-dn.net/?f=s%3D3.4%5Ctimes%20%5C%204.5radians)
thus s = 15.3 inches
Answer:
Count the dots but instead as a Fraction. Like one dot is the fraction the line is on. Add them together to get your answer
Step-by-step explanation:
Hope this helped :D
Solution:
As per the problem we have
Jason baked 7 pans of brownies he gave 1/4 of the brownies to his two sisters.
we have been asked to find
How many pans of brownies did he give to his sisters.
we can find this by dividing the 7 by 1/4, because this is the exact portion that Jason gave to his sister.
Jason gave
pans of brownies to his sister.
or
Jason gave
pans of brownies to his sister.