Problem
9. $[-/ 7$ Points] DETAILS SCALC9 4.3.030.MI.SA. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. 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 Submit Skip (you cannot come back). Need Help? Read It Submit Answer
Solution
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 \(\boxed{0.533333333333333}\).
