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\displaystyle  \int_1^2 \frac{(x+3)^2}{3} dx\\

 Apr 19, 2022
 #1
avatar+9459 
+2

Using the substitution \(u = x + 3\)\(du = dx\), we have the change of integration boundary \(\begin{cases}x = 1 \implies u= 4\\x = 2 \implies u = 5\end{cases}\). Then we have \(\displaystyle\int_1^2 \dfrac{(x + 3)^2}3\,dx =\dfrac13\int_4^5u^2\,du\). You can use the power rule to integrate it. Note that \(\displaystyle\int_a^b f(x)\,dx = F(b) - F(a)\) where F is an antiderivative of f.

 Apr 19, 2022
 #2
avatar+115 
-5

i need teaching of this pls help

Kakashi  Apr 19, 2022
 #3
avatar+9459 
+1

You can pretty much learn on your own using some online resources.

MaxWong  Apr 19, 2022
 #4
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They are called integrals, and anti- derivatives. you can search them up :)

Guest Apr 19, 2022
 #5
avatar+117872 
+1

Kakashi, you are being a pest.

This mathematics is way over your head and you know that. 

 

Thanks for your answer Max.  

 Apr 19, 2022
edited by Melody  Apr 19, 2022
edited by Melody  Apr 19, 2022

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