Calculus Examples

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

Step 1

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

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

Step 2

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

$\arctan (x)]_{0}^{1}$

Step 3

Evaluate $\arctan (x)$ at $1$ and at $0$ .

$\arctan (1) - \arctan (0)$

Step 4

Simplify.

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Step 4.1

Simplify each term.

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Step 4.1.1

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

$\frac{π}{4} - \arctan (0)$

Step 4.1.2

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

$\frac{π}{4} - 0$

Step 4.1.3

Multiply $- 1$ by $0$ .

$\frac{π}{4} + 0$

Step 4.2

Add $\frac{π}{4}$ and $0$ .

$\frac{π}{4}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{π}{4}$

Decimal Form:

$0.78539816 \dots$

Step 6