Calculus Examples

$\int_{- 0.4772}^{0.4987} x d x$

Step 1

By the Power Rule, the integral of $x$ with respect to $x$ is $\frac{1}{2} x^{2}$ .

$\frac{1}{2} x^{2}]_{- 0.4772}^{0.4987}$

Step 2

Substitute and simplify.

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Step 2.1

Evaluate $\frac{1}{2} x^{2}$ at $0.4987$ and at $- 0.4772$ .

$(\frac{1}{2} \cdot {0.4987}^{2}) - \frac{1}{2} {(- 0.4772)}^{2}$

Step 2.2

Simplify.

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Step 2.2.1

Raise $0.4987$ to the power of $2$ .

$\frac{1}{2} \cdot 0.24870169 - \frac{1}{2} {(- 0.4772)}^{2}$

Step 2.2.2

Combine $\frac{1}{2}$ and $0.24870169$ .

$\frac{0.24870169}{2} - \frac{1}{2} {(- 0.4772)}^{2}$

Step 2.2.3

Raise $- 0.4772$ to the power of $2$ .

$\frac{0.24870169}{2} - \frac{1}{2} \cdot 0.22771984$

Step 2.2.4

Multiply $0.22771984$ by $- 1$ .

$\frac{0.24870169}{2} - 0.22771984 (\frac{1}{2})$

Step 2.2.5

Combine $- 0.22771984$ and $\frac{1}{2}$ .

$\frac{0.24870169}{2} + \frac{- 0.22771984}{2}$

Step 2.2.6

Move the negative in front of the fraction.

$\frac{0.24870169}{2} - \frac{0.22771984}{2}$

Step 2.2.7

Combine the numerators over the common denominator.

$\frac{0.24870169 - 0.22771984}{2}$

Step 2.2.8

Subtract $0.22771984$ from $0.24870169$ .

$\frac{0.02098185}{2}$

Step 3

Divide $0.02098185$ by $2$ .

$0.01049092$

Step 4