Calculus Examples

$- \csc^{2} (θ)$

Step 1

Write $- \csc^{2} (θ)$ as a function.

$f (θ) = - \csc^{2} (θ)$

Step 2

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

$F (θ) = \int f (θ) d θ$

Step 3

Set up the integral to solve.

$F (θ) = \int - \csc^{2} (θ) d θ$

Step 4

Since $- 1$ is constant with respect to $θ$ , move $- 1$ out of the integral.

$- \int \csc^{2} (θ) d θ$

Step 5

Since the derivative of $- \cot (θ)$ is $\csc^{2} (θ)$ , the integral of $\csc^{2} (θ)$ is $- \cot (θ)$ .

$- (- \cot (θ) + C)$

Step 6

Simplify the answer.

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Simplify.

$- - \cot (θ) + C$

Simplify.

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Multiply $- 1$ by $- 1$ .

$1 \cot (θ) + C$

Multiply $\cot (θ)$ by $1$ .

$\cot (θ) + C$

Step 7

The answer is the antiderivative of the function $f (θ) = - \csc^{2} (θ)$ .

$F (θ) =$ $\cot (θ) + C$