Calculus Examples

$\int_{0}^{\frac{π}{4}} 8 \sec^{2} (t) d t$

Step 1

Since $8$ is constant with respect to $t$ , move $8$ out of the integral.

$8 \int_{0}^{\frac{π}{4}} \sec^{2} (t) d t$

Step 2

Since the derivative of $\tan (t)$ is $\sec^{2} (t)$ , the integral of $\sec^{2} (t)$ is $\tan (t)$ .

$8 (\tan (t)]_{0}^{\frac{π}{4}})$

Step 3

Simplify the answer.

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Step 3.1

Evaluate $\tan (t)$ at $\frac{π}{4}$ and at $0$ .

$8 (\tan (\frac{π}{4}) - \tan (0))$

Step 3.2

Simplify.

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Step 3.2.1

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

$8 (1 - \tan (0))$

Step 3.2.2

The exact value of $\tan (0)$ is $0$ .

$8 (1 - 0)$

Step 3.2.3

Multiply $- 1$ by $0$ .

$8 (1 + 0)$

Step 3.2.4

Add $1$ and $0$ .

$8 \cdot 1$

Step 3.2.5

Multiply $8$ by $1$ .

$8$