Calculus Examples

$f (x) = 4 \cos (t) + \sec^{2} (t)$

Step 1

The function $F (x)$ can be found by finding the indefinite integral of the derivative $f (x)$ .

$F (x) = \int f (x) d x$

Step 2

Set up the integral to solve.

$F (x) = \int 4 \cos (t) + \sec^{2} (t) d x$

Step 3

Apply the constant rule.

$(4 \cos (t) + \sec^{2} (t)) x + C$

Step 4

The answer is the antiderivative of the function $f (x) = 4 \cos (t) + \sec^{2} (t)$ .

$F (x) =$ $(4 \cos (t) + \sec^{2} (t)) x + C$