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If g(x)= (x-1)(x-2)  then find \int g(x)dx 

 

 

 

  • Option 1)

    \frac{x^{3}}{2}-\frac{3x^{2}}{2}+x+C

  • Option 2)

    \frac{x^{3}}{3}-\frac{3x^{2}}{2}+x/2+C

  • Option 3)

    \frac{x^{3}}{3}-\frac{3x^{2}}{2}+x+C

  • Option 4)

    \frac{x^{3}}{2}-\frac{3x^{2}}{2}+2x+C

 

Answers (1)

best_answer

As we have learned

Sum/difference rule for integration -

\int \left ( f_{1}\left ( x \right )\pm f_{2}\left ( x \right ) \pm \cdot \cdot \cdot f_{n}\left ( x \right )\right )dx = \int f_{1}\left ( x \right )dx\pm \int f_{2}\left ( x \right )dx\pm \int f_{3}\left ( x \right )dx . . .

-

 

 

=\int ((x^{2})-3x++2)dx = \int (x^{2})dx-3\int xdx+2\int dx

= \frac{x^{3}}{3}-\frac{3x^{2}}{2}+2x+C


Option 1)

\frac{x^{3}}{2}-\frac{3x^{2}}{2}+x+C

This is incorrect

Option 2)

\frac{x^{3}}{3}-\frac{3x^{2}}{2}+x/2+C

This is incorrect

Option 3)

\frac{x^{3}}{3}-\frac{3x^{2}}{2}+x+C

This is incorrect

Option 4)

\frac{x^{3}}{2}-\frac{3x^{2}}{2}+2x+C

This is correct

Posted by

prateek

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