 Hello and welcome to the session. I'm Shashi and I'm going to help you with the following question. Question says, find an antiderivative of the following functions by the method of inspection. First given function is sin 2x. First of all, let us understand what is integration by the method of inspection. To find an antiderivative of a given function, let's say, we are given a function f dash x and we have to find antiderivative of this function. With respect to x, then we will search for a function whose derivative is the given function. We know derivative of fx is f dash x. So antiderivative of f dash x with respect to x is equal to fx. So we can say the search for the required function for finding an antiderivative is known as integration by the method of inspection. Here we have searched the function whose derivative is f dash x and this function is antiderivative of given function f dash x. Now we will use this as our key idea to solve the given question. Let us now start with the solution. Now we have to find antiderivative of sin 2x. Now we will look for a function whose derivative is sin 2x. Now we know derivative of cos 2x is equal to minus 2 sin 2x. Now dividing both the sides of this expression by minus 1 upon 2 we get minus 1 upon 2 multiplied by d by dx of cos 2x is equal to sin 2x. Now we know minus 1 upon 2 multiplied by d by dx of cos 2x is equal to d by dx of minus 1 upon 2 cos 2x. Clearly we can see from this expression that derivative of minus 1 upon 2 cos 2x is equal to sin 2x. So we can see an antiderivative of sin 2x is minus 1 upon 2 cos 2x. So this is our required answer. This completes the session. Hope you understood the solution. Take care and have a nice day.