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If f(x) = e^{x}, F(x)= \int f(x)\;dx and F(1) = 0, then F(x) = ?

  • Option 1)

    e^{x} + e

  • Option 2)

    e^{x}

  • Option 3)

    e^{x} -e

  • Option 4)

    e^{x} +1

 

Answers (1)

best_answer

 

Constant of integration: -

\frac{\mathrm{d} }{\mathrm{d} x}\left ( F\left ( x \right )+C \right )=\frac{\mathrm{d} }{\mathrm{d} x}F \left ( x \right )+0=f\left ( x \right )

Hence    \int f\left ( x \right )dx=F\left ( x \right )+C

- wherein

Where C is the constant of integration .

 

 \\*F(x) = \int e^{x}dx \\*F(x) = e^{x} + c \\* F(1) = e^{1} + c = 0 \Rightarrow c = -e

 


Option 1)

e^{x} + e

Option 2)

e^{x}

Option 3)

e^{x} -e

Option 4)

e^{x} +1

Posted by

gaurav

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