1

My textbook says that integrals of the form $\int R(\sin x,\cos x)$ can be simplified using some substitutions (like $\tan \frac{x}{2}=t $. My question is would those substitutions be applicable if R is just a function of $\sin x$ without any term of $\cos x$ or vice versa? For example if we have to integrate $ \frac {1}{1-\cos^4x}$ in terms of $dx$

Or in a more general case if $R(x,y)$ is a function would $5x$ or $10y^2+2$ be an element of the function?

Mittens
  • 39,145
Tatai
  • 755
  • 4
  • 24
  • 2
    $f(x) = 4$ is a function of $x$ yet is independent of x. Similiar logic applies to your question – egglog Jul 30 '21 at 15:32
  • 1
    Have you heard of constant functions? $f(x) = 0$ is a perfectly valid function of $x$ even if the $x$ doesn't figures in the expression $0$. In the same way, $f(x,y) = 5x$ is a valid function – jjagmath Jul 30 '21 at 15:32
  • @egglog thank you – Tatai Jul 30 '21 at 15:45

0 Answers0