Question

To determine the value of the integral function.

Short answer

The value of the integral is \(\frac{9}{{10}}\).

Step-by-step solution

Given data

The integral function is \(\int_0^1 {\left( {1 - {x^9}} \right)} dx\).

The region lies between \(x = 0\) and \(x = 1\).

Concept used of Integral

Integral of a function\(f(x)\)is denoted as\(\int_a^b f (x)dx\)

Simplify the function

The expression to find the integral value is shown below:

\(\begin{aligned}{c}\int_0^1 {\left( {1 - {x^9}} \right)} dx &= \left( {x - \frac{{{x^{10}}}}{{10}}} \right)_0^1\\ &= \left( {1 - \frac{{{1^{10}}}}{{10}}} \right) - \left( {(0) - \frac{{{{(0)}^{10}}}}{{10}}} \right)\\ &= \left( {\frac{{10 - 1}}{{10}}} \right) - 0\\ &= \frac{9}{{10}}\end{aligned}\)

Therefore, the value of the integral is \(\frac{9}{{10}}\).