How Do I Integrate 2x Dx? - Math Forums

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You are using an out of date browser. It may not display this or other websites correctly.You should upgrade or use an alternative browser. How do i integrate 2x dx?
  • Thread starter gen_shao
  • Start date Jul 9, 2013
  • Tags integrate
G

gen_shao

Joined Jun 2013 42 Posts | 0+ im still confused in integrating. udu = u^n+1/n+1 but the derivative of 2x is 2dx 1/2 S 2x(2dx) so we put 1/2 before integrand sign to compensate for the 2 1/2 S (2x^2)/2 by power formula x is sqaured and divided by 2. the answer is 1/2(x^2) + C .... i tried deriving it but it becomes different.. someone help can someone explain this to me why this doesn't work even if i applied the rules of integrating?? P

Pero

Joined Jun 2013 1K Posts | 116+ London, England You need to ask: what function do you differentiate to get the function you are integrating? So, if you want to integrate the function 2x, you have to find a function whose derivative is 2x. In this case, the derivative of x^2 (plus any constant) is 2x. That's it. If you want to integrate x, then you need half of the function above: the derivative of (x^2)/2 is x. So, the integral of x is (x^2)/2. The trick is that you are working backwards. Perhaps try this. Write down a list of some functions and their derivatives in two columns. The first column is "function" and the second is "derivative". Then, change the headings to "Integral" and "Function" and you've got a list of integrals of some functions without doing any integration! H

HallsofIvy

Joined Sep 2007 2K Posts | 7+
gen_shao said: im still confused in integrating. udu = u^n+1/n+1 but the derivative of 2x is 2dx Click to expand...
Not relevant. You want to integrate not differentiate. What is relevant is that the derivative of x^2 is 2x\,dx That should tell you immediately that the integral of 2x\,dx is x^2+ C .
1/2 S 2x(2dx) so we put 1/2 before integrand sign to compensate for the 2. 1/2 S (2x^2)/2 by power formula x is sqaured and divided by 2. Click to expand...
No, you do NOT want "2dx" because you do not have the derivative of 2x.
the answer is 1/2(x^2) + C .... i tried deriving it but it becomes different.. someone help can someone explain this to me why this doesn't work even if i applied the rules of integrating?? Click to expand...
Your basic "logic" is mixed up. G

gen_shao

Joined Jun 2013 42 Posts | 0+ well.. none of you really helped... BTW i finally know why that didnt work its because when integrating the constant must be written before the integrand sign 2xdx 2 S xdx now.. u and du are coorect.. apply power formula 2 (x^2/2) +c x^2 +c this is the answer H

HallsofIvy

Joined Sep 2007 2K Posts | 7+ Which is exactly what both Pero and I said. I am sorry that you did not understand. M

markaltman

Joined Oct 2017 9 Posts | 0+ Texas To Integrate 2x dx = ∫ 2x dx = 2 ∫ x dx Using integration formula ∫ x^n dx = x^n+1 / n+1 = 2 (x^2/2) + C = x^2 + C Login or Register / Reply

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