0
$\begingroup$

Complete the integrals

  1. $\displaystyle\int \frac{\sin(x)dx}{\sin(x)+\cos(x)}$

  2. $\displaystyle\int_{0}^{\infty } x^{-5}\sin(x)dx$

Find the following limit

$\displaystyle\lim_{x \to \infty } \frac{x^{3}+\sin^{3}x}{x^{3}+\cos^{3}x}$

Thanks!

  • 3
    Two things: 1) Your title is not very helpful. 2) Try to describe what you have tried yourself, where you're stuck and so on.2011-12-19
  • 0
    In the limit above, i try to divide x^3 and get trouble with sin^3(x)/x^3 and cos^3(x)/x^3 from x to inf.2011-12-19
  • 0
    I don't have any solution with the integrals, need some hints...2011-12-19
  • 0
    You almost did the limit. Divide top and bottom by $x^3$. Note that $\frac{\sin^3 x}{x^3}$ and $\frac{\cos^3 x}{x^3}$ both approach $0$, since our trig functions stay between $-1$ and $1$, get crushed on division by $x^3$.2011-12-19
  • 0
    Try wolphram alpha :D http://www.wolframalpha.com/input/?i=%28x^-5%29*%28sin+x%29 Paste the whole link, it will solve all your problems :)2011-12-19
  • 0
    I tried but not understand it... For example with the 1st integral, i used and it make me crazy :(2011-12-19
  • 0
    I dont think so..just type "integral ((sin x)/((sin x)+(cos x)))" and after the answer pops up, cluck on the tab "show steps".2011-12-19
  • 0
    it's very long... i think there will be another way to make it more simple.2011-12-19
  • 0
    @Kiris: It can be made shorter, but only with a trick. Are you sure it is not a *definite* integral that is asked for?2011-12-19

1 Answers 1