Trigonometric Integrals Examples
For this type of integral, you're dealing with an odd power of sine and an even power of cosine, which suggests that using trigonometric identities is the way to approach the problem. A helpful technique here is to save one sine factor to work with later and rewrite the rest using an identity that relates sine and cosine.
You can express the even power of cosine using the identity for cosine squared, which will allow you to convert the integral into something involving sine functions only. Once you've done that, you can make a substitution where you treat sine as your new variable, allowing you to integrate the remaining terms more easily.
After simplifying and carrying out the substitution, the integration becomes more straightforward, leading to the solution. This method of using identities and substitution is a common approach when you're faced with products of sine and cosine raised to powers.
Related Problems
Evaluate the integral .
Evaluate using the double angle identity.
Evaluate the integral of which is equivalent to the inverse sine of x.
Solve using the substitution method where the power of sine is odd.