 Hello and how are you all doing today? My name is Priyanka and I shall be helping you with the following question. Here the question says integrate the following. Now the function which is given to us is sin 3x cos 4x. Here we need to find out the integral of sin 3x cos 4x. Now here we must remember that the formula for sin a cos b is equal to 1 by 2 sin a plus b plus sin a minus b. Now here we will be using the knowledge of this formula to find out the integral of sin 3x cos 4x dx and that is equal to 1 by 2 integral of here sin a plus b where a is 3x and b is 4x will be sin 7x plus sin a minus b will be 3x minus 4x that gives us minus x that is further equal to 1 by 2 into integral of sin 7x plus 1 by 2 into integral of sin minus x dx which is further equal to 1 by 2 integral of sin 7x dx will be equal to minus cos 7x divided by the differentiation of 7x that is 7 plus 1 by 2 sin minus x can be written as minus sin x dx. Now we have 1 by 14 that is minus 1 by 14 cos 7x minus 1 by 2 this minus sin will come out of the integral and we have the integral of sin x as minus cos x plus c and the required answer will be minus 1 by 14 cos 7x plus 1 by 2 cos x plus c. So this is the required answer to the session. Hope you understood and enjoy it to have a nice day.