The integral of sec theta tan theta is sec theta.
Here's why:
- The derivative of sec theta is sec theta tan theta. This is a fundamental trigonometric identity.
- Integration is the reverse process of differentiation. Therefore, if the derivative of sec theta is sec theta tan theta, then the integral of sec theta tan theta must be sec theta.
Example:
Let's say we want to find the integral of sec x tan x dx.
- We know that the derivative of sec x is sec x tan x.
- Therefore, the integral of sec x tan x dx is simply sec x + C, where C is the constant of integration.
Practical Insights:
This integral appears frequently in calculus problems involving trigonometric functions. Understanding this relationship between sec theta tan theta and sec theta is crucial for solving these problems.
In summary:
The integral of sec theta tan theta is sec theta. This relationship stems from the fundamental trigonometric identity that the derivative of sec theta is sec theta tan theta.
