Calculus Examples

$\int_{0}^{π} \frac{4}{x^{2} + 1} d x$

Step 1

Since $4$ is constant with respect to $x$ , move $4$ out of the integral.

$4 \int_{0}^{π} \frac{1}{x^{2} + 1} d x$

Step 2

Simplify the expression.

Tap for more steps...

Step 2.1

Reorder $x^{2}$ and $1$ .

$4 \int_{0}^{π} \frac{1}{1 + x^{2}} d x$

Step 2.2

Rewrite $1$ as $1^{2}$ .

$4 \int_{0}^{π} \frac{1}{1^{2} + x^{2}} d x$

Step 3

The integral of $\frac{1}{1^{2} + x^{2}}$ with respect to $x$ is $\arctan (x)]_{0}^{π}$ .

$4 (\arctan (x)]_{0}^{π})$

Step 4

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

$4 (\arctan (π) - \arctan (0))$

Step 5

Simplify.

Tap for more steps...

Step 5.1

Simplify each term.

Tap for more steps...

Step 5.1.1

Evaluate $\arctan (π)$ .

$4 (1.26262725 - \arctan (0))$

Step 5.1.2

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

$4 (1.26262725 - 0)$

Step 5.1.3

Multiply $- 1$ by $0$ .

$4 (1.26262725 + 0)$

Step 5.2

Add $1.26262725$ and $0$ .

$4 \cdot 1.26262725$

Step 5.3

Multiply $4$ by $1.26262725$ .

$5.05050902$

Step 6