I just don't understand what I'm doing wrong. I'm doing it exactly like it was taught to me but I'm getting a completely different answer from the correct answer.


My work:



substitute $\cos(x)$ for $u$.





$$\frac{1}{15}\cos^{15}\left(\frac{\pi}{2}\right)-\frac{2}{17}\cos^{17}\left(\frac{\pi}{2}\right)+\frac{1}{19}\cos^{19}\left(\frac{\pi}{2}\right) - \left(\frac{1}{15}\cos^{15}(0)-\frac{2}{17}\cos^{17}(0)+\frac{1}{19}\cos^{19}(0)\right)$$



The correct answer is $\frac{8}{4845}$

Where did I go wrong?


It is in fact $u=-\cos x$ and by substitution we get $$\frac{1}{15}u^{15}-\frac{2}{17}u^{17}+\frac{1}{19}u^{19}\Bigg|_{-1}^0={1\over 15}-{2\over 17}+{1\over 19}={8\over 4845}$$You where only wrong in substitution...

  • $\begingroup$ And I forgot to multiply the 1 by the fractions... I feel stupid. Thank you for the help. $\endgroup$ – Haruku Mar 18 at 11:09
  • $\begingroup$ Your welcome. Good luck!! $\endgroup$ – Mostafa Ayaz Mar 18 at 11:10

$$u = \cos x$$ $$du = -\sin x \,dx$$

(and not $du = \sin x \,dx$, as you wrote).


There are other errors in your calculation. But they cancel each other out. If you make a substitution and you have limits of integration then you have to transform these limits too. So if the substitution is $$u=\cos(x)$$ then the limit of integration change to



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