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DETAILS SCALC9 4.3.030.MI.SA.
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Tutorial Exercise
Evaluate the integral.
\[
\int_{0}^{1} x^{7 / 8} d x
\]
Step 1
An antiderivative of $x^{n}$, as long as $n \neq-1$, is
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Answer
The value of the integral \(\int_{0}^{1} x^{7 / 8} d x\) is \(\boxed{0.533333333333333}\).
Step 1 ：An antiderivative of \(x^{n}\), as long as \(n \neq-1\), is \(\frac{x^{n+1}}{n+1}\).
Step 2 ：In this case, the function is \(x^{7/8}\), so we can apply this rule directly.
Step 3 ：The antiderivative of \(x^{7/8}\) is \(0.533333333333333*x^{1.875}\).
Step 4 ：We will then evaluate the antiderivative at the upper limit of integration (1) and subtract the value of the antiderivative at the lower limit of integration (0).
Step 5 ：The value of the integral \(\int_{0}^{1} x^{7 / 8} d x\) is \(\boxed{0.533333333333333}\).
