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  • Need clarity, kindly explain! - Integral Calculus - JEE Main-13

Find the integral \int e^{2x}\sin 2xdx + \int e^{2x}\cos 2x dx

  • Option 1)

    e^{2x}\sin 2x+ C

  • Option 2)

    2e^{2x}\sin 2x+ C

  • Option 3)

    (e^{2x}\sin 2x)/2+ C

  • Option 4)

    none of these

 

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^{2x}(\sin 2x+ d/dx (\sin2x)/2) dx

=\frac{e^{2x}\sin 2x}{2}+c 

 

 

 

 


Option 1)

e^{2x}\sin 2x+ C

Option 2)

2e^{2x}\sin 2x+ C

Option 3)

(e^{2x}\sin 2x)/2+ C

Option 4)

none of these

Posted by

Aadil

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