### Video Transcript

Determine the integral of negative four times the cos of nine π₯ with respect to π₯.

Weβre asked to evaluate the integral of a trigonometric function. And we can do this by recalling our rules for integrating trigonometric functions. We recall for any real constants π and π where π is not equal to zero, the integral of π times the cos of ππ₯ with respect to π₯ is equal to π times the sin of ππ₯ divided by π plus the constant of integration πΆ. Integrals of this form come up a lot, so itβs worth committing these to memory.

We want to apply this to the integral given to us in the question. We can see our value of the constant π is negative four and the value of the constant π is nine. So by setting π equal to negative four and π equal to nine into our integral result, we get that our integral is equal to negative four sin of nine π₯ all divided by nine. And remember, we need to add our constant of integration πΆ. And weβll rewrite this as negative four over nine times the sin of nine π₯ plus πΆ.

Therefore, by using our standard trigonometric integral results, we were able to show the integral of negative four times the cos of nine π₯ with respect to π₯ is equal to negative four over nine times the sin of nine π₯ plus πΆ.