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  • I have a doubt, kindly clarify. - Integral Calculus - JEE Main-11

Evaluate  \int e^{3x}(3 \sin x + \cos x )dx

  • Option 1)

    e^{3x} \cos x + C

  • Option 2)

    \frac{e^{3x}\cos x}{3}+C

  • Option 3)

    e^{3x} \sin x + C

  • Option 4)

    \frac{e^{3x} \sin x }{3} + C

 

Answers (1)

best_answer

As we have learned

Result for integration by parts -

\int e^{ax} \left (f(x)+\frac{f'(x)}{a}dx\right ) = \frac{e^{ax}f(x)}{a}+c

  

- wherein

Put ax=t 

dx=\frac{dt}{a}

 

 \int e^{3x}(3sin x + \cos x)dx

=3\int e^{3x}(3sin x + \cos x/3)dx

=3*e^{3x}\sin x/3+C = e^{3x} \sin x +C

 

 

 


Option 1)

e^{3x} \cos x + C

This is incorrect

Option 2)

\frac{e^{3x}\cos x}{3}+C

This is incorrect

Option 3)

e^{3x} \sin x + C

This is correct

Option 4)

\frac{e^{3x} \sin x }{3} + C

This is incorrect

Posted by

gaurav

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