`h(theta) = 2sin(theta) - sec^2 (theta)` Find the most general antiderivative of the function.

Expert Answers
sciencesolve eNotes educator| Certified Educator

The most general antiderivative `H(theta)` of the function `h(theta)` can be found using the following relation:

`int h(theta)d theta = H(theta) + c`

`int (2sin theta - sec^2 theta)d theta = int (2sin theta)d theta - int (sec^2 theta)d theta`

You need to use the following formulas:

`intsin theta d theta = -cos theta + c => int (2sin theta)d theta = -2cos theta + c`

`sec^2 theta = 1/(cos^2 theta) = (tan theta)' => int sec^2 theta d theta = int (tan theta)' = tan theta + c`

Gathering all the results yields:

`int (2sin theta - sec^2 theta)d theta =-2cos theta - tan theta + c`

Hence, evaluating the most general antiderivative of the function yields `H(theta) = -2cos theta - tan theta + c` .