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GuDViN [60]
3 years ago
15

Plz help on the 6 problems

Mathematics
1 answer:
Leokris [45]3 years ago
5 0
1.) 9
2.)7
3.)106
4.)13
5.)192
6.)11
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Find the indefinite integral. (Note: Solve by the simplest method—not all require integration by parts. Use C for the constant o
umka2103 [35]

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)

3 0
3 years ago
Read 2 more answers
Brent is trying to figure out the relationship between the number of times his friends post on social media and their grade poin
andrew11 [14]

The given graph shows the relationship between the social media posts and grade point average of different students in Brent's class.

From the given graph, we can say that the grade point average of students decrease with increase in number of their social media posts.  

Since grade point average decreases approximately linearly with increase in use of social media posts, It is Strong negative correlation.

Hence, option D is correct i.e. Strong Negative Correlation.

5 0
3 years ago
Read 2 more answers
What times what equals 152
erik [133]

x*x=152


x2=152

Take square root.

x=±√152

x=√238
or
x=−√238

7 0
3 years ago
Find the perimeter of this figure. Enter your answer in the box.
diamong [38]

Answer:

56 total units

Step-by-step explanation:

Here is what the plane would look like if the figure and points were drawn.

3 0
2 years ago
Read 2 more answers
You use about 15 gallons of water when you shower. If you take 20% less time when you shower, estimate how many gallons of water
PIT_PIT [208]
I would have to say 85 but thats just a guess.
8 0
3 years ago
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