title: Definite, improper and multiple integration?
body: <p>I have a question, whether is it possible in R to implement the Excel "search of the decision function"?  It is necessary to create a script in R to solve an integral equation.</p>
  
  <p>To solve 4 integrals below manually I just need paper, a pencil and 10 minutes:</p>
  
  <p><em>Improper:</em></p>
  
  <p><img src="https://i.stack.imgur.com/Nx54k.png" width="200" /></p>
  
  <p><em>Double:</em></p>
  
  <p><img src="https://i.stack.imgur.com/OZngz.png" width="400" /></p>
  
  <p><em>Triple:</em></p>
  
  <p><img src="https://i.stack.imgur.com/UtTQY.png" width="600" /></p>
  
  <p><em>Definite:</em></p>
  
  <p><img src="https://i.stack.imgur.com/FXdAt.png" width="400" /></p>
  
  <p>So I don't want solve the integrals like these manually, how can it be solved using R?</p>
  
  <p><a href="https://www.latex4technics.com/" rel="nofollow noreferrer">LATEX formala editor</a> code:</p>
  
  <pre><code>improper
  \int_{2}^{\infty} \frac{1}{\left(x - 1\right)^{2}}\, dx
  
  
  double integrals
  \int_{0}^{1}\int_{\frac{-1 x}{2}}^{\frac{x}{2}} e^{- x - y}\, dy\, dx
  
  triple integrals
  \int_{0}^{1}\int_{\frac{-1 x}{2}}^{\frac{x}{2}}\int_{\frac{-1 y}{3}}^{\frac{y}{3}} e^{- z + - x - y}\, dz\, dy\, dx
  
  definite integrals
  \int_{0}^{1} x^{2} \sin{\left (x \right )}\, dx
  </code></pre>