Calculus Examples

$\int_{0}^{π} \sec (x) \tan (x) d x$

Step 1

Since the derivative of $\sec (x)$ is $\sec (x) \tan (x)$ , the integral of $\sec (x) \tan (x)$ is $\sec (x)$ .

$\sec (x)]_{0}^{π}$

Step 2

Simplify the answer.

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Step 2.1

Evaluate $\sec (x)$ at $π$ and at $0$ .

$\sec (π) - \sec (0)$

Step 2.2

Simplify.

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Step 2.2.1

The exact value of $\sec (0)$ is $1$ .

$\sec (π) - 1 \cdot 1$

Step 2.2.2

Multiply $- 1$ by $1$ .

$\sec (π) - 1$

Step 3

Simplify.

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Step 3.1

Simplify each term.

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Step 3.1.1

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because secant is negative in the second quadrant.

$- \sec (0) - 1$

Step 3.1.2

The exact value of $\sec (0)$ is $1$ .

$- 1 \cdot 1 - 1$

Step 3.1.3

Multiply $- 1$ by $1$ .

$- 1 - 1$

Step 3.2

Subtract $1$ from $- 1$ .

$- 2$