Video: Integrating Trigonometric Functions

Determine ∫ βˆ’4 cos 9π‘₯ dπ‘₯.

01:12

Video Transcript

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

We’re 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‘Ž and π‘˜ where π‘Ž is not equal to zero, the integral of π‘˜ times the cos of π‘Žπ‘₯ with respect to π‘₯ is equal to π‘˜ times the sin of π‘Žπ‘₯ divided by π‘Ž plus the constant of integration 𝐢. Integrals of this form come up a lot, so it’s 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‘Ž is nine. So by setting π‘˜ equal to negative four and π‘Ž 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 𝐢. And we’ll rewrite this as negative four over nine times the sin of nine π‘₯ plus 𝐢.

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 𝐢.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.