Integral of sine squared x dx
For this integral, you're dealing with a trigonometric function squared, which is a common type of problem in calculus. The key approach here is to use a trigonometric identity to simplify the expression before integrating. Specifically, when you have a squared sine or cosine function, you can apply a well-known identity to rewrite the integral in a more manageable form.
The identity that is typically useful here is the power-reduction identity, which expresses the square of the sine function in terms of a cosine function. By using this identity, you turn the squared sine into a simpler trigonometric function that can be integrated more easily. Once you've rewritten the integral using this identity, you can then proceed with the integration, which becomes straightforward.
This problem illustrates how applying the right trigonometric identities can simplify more complicated integrals involving squared functions, allowing you to solve them step by step. This method will come up frequently in integration problems involving trigonometric functions.