Mathematics∫ln2ln3xsin x 2sin x 2+ sin (ln 6- x2 )  dx is ____.  

ln2ln3xsin x 2sin x 2+ sin (ln 6- x2 )  dx is ____.  


    Fill Out the Form for Expert Academic Guidance!l



    +91



    Live ClassesBooksTest SeriesSelf Learning



    Verify OTP Code (required)

    I agree to the terms and conditions and privacy policy.

    Solution:

    Let,
    I= ln2ln3xsin x 2sin x 2+ sin (ln 6- x2 )  dx 

    Put x2=t
    2xdx=dt
    The integral will transform into
    I=ln2ln312sintsin x 2+ sin (ln 6- t )  dx 
    =ln2ln312sin(ln6-t)sin x 2+ sin (ln 6- t )  dx 
    Adding both the equations, we get
       2I= 12ln2ln3sint+sin(ln6-t)sint+sin(ln6-t) dt
     I= 14ln2ln3dt
    I=14[ln3-ln2]
    I=14ln32
    Hence option 1 is correct.
     
    Chat on WhatsApp Call Infinity Learn

      Talk to our academic expert!



      +91


      Live ClassesBooksTest SeriesSelf Learning




      Verify OTP Code (required)

      I agree to the terms and conditions and privacy policy.