Find the general antiderivative of the function below. Use theta for θ.
P(θ) = + C
need help with another one please, just dont know where to begin, any help would be fantastic, thanks
Some hints:
$\displaystyle \frac{d}{dx} \sec \theta = \sec \theta \tan \theta$
$\displaystyle \frac{d}{dx} \tan \theta = \sec^{2} \theta$
Can you see how these apply to your integral? Basically you're going backwards from derivatives you learned in differentiation.
Let me colour code this:
$\displaystyle p(\theta) = {\color{red} \sec \theta \tan \theta } + {\color{blue}\frac{6}{\cos^{2} \theta}}$
$\displaystyle \frac{d}{dx} \sec \theta = {\color{red} \sec \theta \tan \theta }$
$\displaystyle \frac{d}{dx} \tan \theta = {\color{blue}sec^{2} \theta}$**
** Should've been this one in the first post