Evaluate the integral: ∫ − 1 1 x 2 2 d x

Question

Evaluate the integral:      ∫          −      1              1                  x              2              2    d  x

Rebecca Benitez · Accepted Answer

To evaluate the definite integral, first evaluate the indefinite integral:

\int \frac{x^{2}}{2} d x

Notice that there is a constant

\frac{1}{2}

in the integral, so use the property

\int a \times f (x) d x = a \times \int f (x) d x

\frac{1}{2} \int x^{2} d x

Now, use the rule

\int x^{n} = \frac{x^{n + 1}}{n + 1}

\frac{1}{2} \times \frac{x^{3}}{3}

Multiply the fractions:

\frac{x^{3}}{6}

To evaluate the definite integral, return the limits of integration:

(\frac{x^{3}}{6}) |_{0}^{5}

Use

\int_{a}^{b} f (x) d x = F (b) - F (a)

to evaluate the expression:

\frac{1^{3}}{6} - \frac{(- 1)^{3}}{6}

Evaluate the expression:

\frac{1}{3}

Great! The definite integral

\int_{- 1}^{1} \frac{x^{2}}{2} d x

is equal to:

\frac{1}{3}

Evaluate the integral: int_(-1)^(1) /(x^(2))(2)dx