LinkBack URL
About LinkBacksJust wondering about the validity of this answer obtained via using an identity?
A second opinion would be much appreciated! Thanks.
Even though this solution looks fine, it is NOT the most efficient method in this case. I always tell my students to look for obvious substitutions.Originally Posted by DonGorgon
Now letand the integral becomes
![\displaystyle \begin{align*} -\int{-\sin{(x)}\left[ 1 - \cos^2{(x)} \right] dx} &= -\int{ 1 - u^2 \, du } \\ &= - \left( u - \frac{u^3}{3} \right) +C \\ &= -\cos{(x)} + \frac{\cos^3{(x)}}{3} + C \end{align*}](http://latex.codecogs.com/png.latex?\displaystyle \begin{align*} -\int{-\sin{(x)}\left[ 1 - \cos^2{(x)} \right] dx} &= -\int{ 1 - u^2 \, du } \\ &= - \left( u - \frac{u^3}{3} \right) +C \\ &= -\cos{(x)} + \frac{\cos^3{(x)}}{3} + C \end{align*})
  |
