Calculus Examples

$\int_{- 4}^{- 1} \frac{π}{2} d θ$

Step 1

Apply the constant rule.

$\frac{π}{2} θ]_{- 4}^{- 1}$

Step 2

Substitute and simplify.

Tap for more steps...

Step 2.1

Evaluate $\frac{π}{2} θ$ at $- 1$ and at $- 4$ .

$(\frac{π}{2} \cdot - 1) - \frac{π}{2} \cdot - 4$

Step 2.2

Simplify.

Tap for more steps...

Step 2.2.1

Combine $\frac{π}{2}$ and $- 1$ .

$\frac{π \cdot - 1}{2} - \frac{π}{2} \cdot - 4$

Step 2.2.2

Move $- 1$ to the left of $π$ .

$\frac{- 1 \cdot π}{2} - \frac{π}{2} \cdot - 4$

Step 2.2.3

Rewrite $- 1 π$ as $- π$ .

$\frac{- π}{2} - \frac{π}{2} \cdot - 4$

Step 2.2.4

Move the negative in front of the fraction.

$- \frac{π}{2} - \frac{π}{2} \cdot - 4$

Step 2.2.5

Multiply $- 4$ by $- 1$ .

$- \frac{π}{2} + 4 \frac{π}{2}$

Step 2.2.6

Combine $4$ and $\frac{π}{2}$ .

$- \frac{π}{2} + \frac{4 π}{2}$

Step 2.2.7

Cancel the common factor of $4$ and $2$ .

Tap for more steps...

Step 2.2.7.1

Factor $2$ out of $4 π$ .

$- \frac{π}{2} + \frac{2 (2 π)}{2}$

Step 2.2.7.2

Cancel the common factors.

Tap for more steps...

Step 2.2.7.2.1

Factor $2$ out of $2$ .

$- \frac{π}{2} + \frac{2 (2 π)}{2 (1)}$

Step 2.2.7.2.2

Cancel the common factor.

$- \frac{π}{2} + \frac{2 (2 π)}{2 \cdot 1}$

Step 2.2.7.2.3

Rewrite the expression.

$- \frac{π}{2} + \frac{2 π}{1}$

Step 2.2.7.2.4

Divide $2 π$ by $1$ .

$- \frac{π}{2} + 2 π$

$- \frac{π}{2} + 2 π$

$- \frac{π}{2} + 2 π$

Step 2.2.8

To write $2 π$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{π}{2} + 2 π \cdot \frac{2}{2}$

Step 2.2.9

Combine $2 π$ and $\frac{2}{2}$ .

$- \frac{π}{2} + \frac{2 π \cdot 2}{2}$

Step 2.2.10

Combine the numerators over the common denominator.

$\frac{- π + 2 π \cdot 2}{2}$

Step 2.2.11

Multiply $2$ by $2$ .

$\frac{- π + 4 π}{2}$

Step 2.2.12

Add $- π$ and $4 π$ .

$\frac{3 π}{2}$

$\frac{3 π}{2}$

$\frac{3 π}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{3 π}{2}$

Decimal Form:

$4.71238898 \dots$

Step 4

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$