QuestionFind the integral of $\sec^{2} \theta$ with respect to $\theta$ .

Studdy Solution

STEP 1

Assumptions1. We are asked to integrate the function $\sec^ \theta$ with respect to $\theta$ . . The integral of a function is the area under the curve of the function.
3. We are looking for the antiderivative of $\sec^ \theta$ , which is a function whose derivative is $\sec^ \theta$ .

STEP 2

We know from the standard integral formulas that the antiderivative of $\sec^2 \theta$ is $\tan \theta$ . So we can write $\int \sec^2 \theta \, d\theta = \tan \theta + C$ where $C$ is the constant of integration.

STEP 3

So, the solution to the integral $\int \sec^2 \theta \, d\theta$ is $\tan \theta + C$ .

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