text: Choose indefinite or definite integral
  
  I have an equation like this
  
  $dW=x\,dx$ , where W is work.
  
  I have find a lot on internet, but I wasn't able to find clear information. I have two questions:
  
  1) If I want to integrate this equation, do im forced to apply definite integral or indefinite integral at the same time to each member of the equation ?
  
  2)The right part of the integral is quite clear to me, for example I can integrate between $x=0$ and $x=5$. But in the left part, what's the meaning to integrate between (for example) $W=4$ and $W=8$ ?
  
  If you are finding the work between two points you can integrate the right hand side from between any values of $x$.
  and the left hand side between any values of $x$ as W is a function of$x$.
  That being said , if you are integrating from$2$to $x$ you'll need to know the initial condition of $W(2)$.
  $W(x) - W(2)=\frac{1}{2}x^2 -2$.
explanation: The document contains a math question with an answer. The user asks about the choice between definite and indefinite integrals when integrating an equation involving work and displacement. The user also inquires about the meaning of integrating between specific values of work. The provided answer clarifies that both sides of the equation should be integrated consistently, and it explains the relationship between the work function and the displacement variable.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: Choose indefinite or definite integral
  
  I have an equation like this
  
  $dW=x\,dx$ , where W is work.
  
  I have find a lot on internet, but I wasn't able to find clear information. I have two questions:
  
  1) If I want to integrate this equation, do im forced to apply definite integral or indefinite integral at the same time to each member of the equation ?
  
  2)The right part of the integral is quite clear to me, for example I can integrate between $x=0$ and $x=5$. But in the left part, what's the meaning to integrate between (for example) $W=4$ and $W=8$ ?
  
  If you are finding the work between two points you can integrate the right hand side from between any values of $x$.
  and the left hand side between any values of $x$ as W is a function of$x$.
  That being said , if you are integrating from$2$to $x$ you'll need to know the initial condition of $W(2)$.
  $W(x) - W(2)=\frac{1}{2}x^2 -2$.
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math question with an answer. The user asks about the choice between definite and indefinite integrals when integrating an equation involving work and displacement. The user also inquires about the meaning of integrating between specific values of work. The provided answer clarifies that both sides of the equation should be integrated consistently, and it explains the relationship between the work function and the displacement variable.
  
  Label: question-and-answer