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  • Confused! kindly explain, - Integral Calculus - JEE Main-12

FInd the value of integral \int (x^{e} + x^{\pi})dx

  • Option 1)

    x^{e} + x^{\pi + 1} + c

  • Option 2)

    x^{e+1} + x^{\pi + 1} + c

  • Option 3)

    x^{e} + x^{\pi} + c

  • Option 4)

    Cant evaluate since e, \pi are irrational numbers.

 

Answers (1)

best_answer

As we have learnt,

 

Indefinite integrals for Algebraic functions -

 \frac{\mathrm{d}}{\mathrm{d} x} \frac{\left ( x^{n+1} \right )}{n+1}=x^{n} so \int x^{n}dx=\frac{x^{n+1}}{n+1}

- wherein

Where  n\neq-1

 

 \int (x^{e}+x^{\pi})= x^{e+1}+x^{\pi + 1} + c

 


Option 1)

x^{e} + x^{\pi + 1} + c

Option 2)

x^{e+1} + x^{\pi + 1} + c

Option 3)

x^{e} + x^{\pi} + c

Option 4)

Cant evaluate since e, \pi are irrational numbers.

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gaurav

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