Calculus Examples

$\int_{\frac{π}{4}}^{\cot (x)} \csc^{2} (y) d y$

Step 1

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

$- \cot (y)]_{\frac{π}{4}}^{\cot (x)}$

Step 2

Simplify the answer.

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Step 2.1

Evaluate $- \cot (y)$ at $\cot (x)$ and at $\frac{π}{4}$ .

$- \cot (\cot (x)) + \cot (\frac{π}{4})$

Step 2.2

The exact value of $\cot (\frac{π}{4})$ is $1$ .

$- \cot (\cot (x)) + 1$