Dick said:You don't have to do anything complicated with it, cos(x)dx=d(sin(x)). Just substitute u=sin(x). There are rules for dealing with powers of sin's and cos's. They are particularly easy if one power is odd.
Dick said:Oh, come on. Just work it out and show us what you get. I'll guarantee someone will check it.
Mugen Prospec said:Ok I have other work to do this one has bee on my mind all night. Ill post it tomorrow when I am clear of thought
Mugen Prospec said:Thats what I was thinking. after using u substitution I was left with
(u)^6 (cos^2(x)) cos(x) du/cos(x)
So cos(x) canceled out.
Mugen Prospec said:Oh ok the identity. so now all turns into
u^7 (1-u^2) du
Do I do their antiderivative now? And then substitute sin(x) back in. I am not sure if you can do each of there AD since they are multiplying one another.
Mugen Prospec said:OK that what I thought I am trying to do this not without witting it down since I am in chemistry.
So we get (u^6)-(u^8)du
then (u^7)/7) - (u^9)/9)
41 (sin^7(x))/7) - (sin^9(x))/9)
is that it maybe?
A trigonometric integral is an integral that involves trigonometric functions, such as sine, cosine, and tangent. These types of integrals are commonly used in calculus to solve problems in geometry, physics, and engineering.
The process for solving a trigonometric integral involves using various integration techniques, such as substitution or integration by parts, as well as trigonometric identities. The goal is to manipulate the integral into a form that can be easily integrated using standard methods.
To solve this specific trigonometric integral, you can use the half-angle formula for cosine to rewrite the integral as a combination of sine and cosine terms. Then, you can use the power-reducing formula for sine to simplify the integral further. Finally, you can use basic integration techniques to solve the remaining integral.
Common mistakes when solving trigonometric integrals include not properly applying trigonometric identities, forgetting to use substitution or integration by parts, and making errors in algebraic simplification. It is important to carefully follow the steps and check your work to avoid these mistakes.
The best way to practice and improve your skills in solving trigonometric integrals is to work through a variety of practice problems, both in your textbook and online. You can also review trigonometric identities and integration techniques to strengthen your understanding. Seeking help from a tutor or attending study groups can also be beneficial.