Answer:
∫▒〖arctan(x).1 dx=arctan(x).x〗-1/2 ln(1+x^2 )+C
Step-by-step explanation:
∫▒〖1st .2nd dx=1st∫▒〖2nd dx〗-∫▒〖(derivative of 1st) dx∫▒〖2nd dx〗〗〗
Let 1st=arctan(x)
And 2nd=1
∫▒〖arctan(x).1 dx=arctan(x) ∫▒〖1 dx〗-∫▒〖(derivative of arctan(x))dx∫▒〖1 dx〗〗〗
As we know that
derivative of arctan(x)=1/(1+x^2 )
∫▒〖1 dx〗=x
So
∫▒〖arctan(x).1 dx=arctan(x).x〗-∫▒〖(1/(1+x^2 ))dx.x〗…………Eq1
Let’s solve ∫▒(1/(1+x^2 ))dx by substitution now
Let 1+x^2=u
du=2xdx
Multiply and divide ∫▒〖(1/(1+x^2 ))dx.x〗 by 2 we get
1/2 ∫▒〖(2/(1+x^2 ))dx.x〗=1/2 ∫▒(2xdx/u)
1/2 ∫▒(2xdx/u) =1/2 ∫▒(du/u)
1/2 ∫▒(2xdx/u) =1/2 ln(u)+C
1/2 ∫▒(2xdx/u) =1/2 ln(1+x^2 )+C
Putting values in Eq1 we get
∫▒〖arctan(x).1 dx=arctan(x).x〗-1/2 ln(1+x^2 )+C (required soultion)
6/12=X/18
Using the ratio of 18:12, you multiply 18/12 with 6, which equals 9.
Answer: NJ=9
Answer:
C. $12.60
Step-by-step explanation:
he has $25.00 for the whole week
monday through thursday, or four days, he buys school lunch for $1.50
1.5 x 4 = 6
on friday, he buys 4 slices of pizza for $1.60 per slice
4 x 1.6 = 6.4
Expenses together:
6.4 + 6 = 12.4
Find what he has left:
25-12.4 = 12.6
C. $12.60
Answer: 
Step-by-step explanation:
First, we need to find the common denominator
The easiest way to do this is by multiplying the two given denominators, which are 2 and 5.
2 × 5 = 10
So, our common denominator is 10. Then, multiply the numerators of the two fractions by 2 and 5. Here's why:
= 
We multiplied the top and bottom by 2 to make sure our new fraction stays equivalent to the original fraction.
Do the same thing for the other one:
= 
Finally, subtract the two fractions to find the difference between the two times:
=
The reason we used the common denominator is because we can only add or subtract fractions if they have the same denominator.
Answer:
80% of the values will occurs above 68.24.
Step-by-step explain
thinking this is right but im sorry if its wrong
