What is #f(x) = int secx-cotx dx# if #f(pi/8) = 0 #?
1 Answer
Use trigonometric identities, u-substitution, and the known derivative formulae for various trig functions.
Explanation:
To find this integral, we will have to rely on some trigonometric tricks.
First, separate the integral into 2 parts:
Now, we must find the integrals of each part. For the first one, we will multiply by
It seems we will use a natural log here, but it helps for us to confirm it.
Differentiate the denominator; if it turns out equal to the numerator, we have a
Thus, we have a
The integral of such an expression is simply
To integrate our second part, the
Here, we already have a
Adding these together, and remembering that c is any constant, we get:
To get rid of the constant, we plug in the term
Thus,