Skip to main content
Mathematics LibreTexts

Integration By Parts Activity

  • Page ID
    89634
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    First Step For Integration By Parts Activity

    An integral will appear at the top and slowly fall down.  Your task is to move the integral to the correct position so that it lands on the correct first step, or on "Impossible" if it cannot be done using substitution or integration by parts.  Click on Get Started to begin.

    \(u=x, dv=\cos(x)\)  \(u=cos(x),  dv = x\)   Substitution          Impossible

    \(u=x, dv=\ln(x)\)   \(u=ln(x),  dv = x\)    Substitution          Impossible

    \(u=x, dv=e^{x^{2}}\)   \(u=e^{x^{2}},  dv = x\)    Substitution          Impossible

    \(u=\frac{1}{x}, dv=\sin(x)\)   \(u=\sin{x},  dv = \frac{1}{x}\)    Substitution          Impossible

    \(u=1, dv=\tan^{-1}(x)\)   \(u=\tan^{-1}(x),  dv =1 \)    Substitution          Impossible

    \(u=x^2, dv=e^x\)   \(u=e^x,  dv =x^2 \)    Substitution          Impossible

    \(u=ln(x), dv=\frac{1}{x}\)   \(u=\frac{1}{x},  dv =ln(x) \)    Substitution          Impossible

    \(u=1, dv=e^{x^2}\)   \(u=e^{x^2},  dv =1 \)    Substitution          Impossible

    \(u=ln(x), dv=\frac{1}{x^{4}}\)   \(u=\frac{1}{x^{4}},  dv =ln(x) \)    Substitution          Impossible

    \(u=1, dv=sin^{-1}(x)\)   \(u=sin^{-1}(x),  dv =1 \)    Substitution          Impossible

                      

    0 Correct and 0 Incorrect

      Happy FaceSad Faceintegral of xCosx dxintegral of xln(x) dxIntegral of x e to the x squared dx Integral of sin(x) over x dxIntegral of arctan(x)dxIntegral of x^2 e^x dxIntegral of ln(x) over xIntegral of e^(x^2)Integral of ln(x)/x^4 dxIntegral of arcsin(x)dx   

     

     


    Integration By Parts Activity is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.

    • Was this article helpful?