To solve the given expression [tex]\(\left. \frac{1}{3} \right|_{3}^{d^3}\)[/tex], let's break it down step by step.
1. Expression Setup:
The notation [tex]\(\left. \frac{1}{3} \right|_{3}^{d^3}\)[/tex] implies that we need to evaluate the expression [tex]\(\frac{1}{3}\)[/tex] from the lower limit [tex]\(x = 3\)[/tex] to the upper limit [tex]\(x = d^3\)[/tex].
2. Insert Limits:
We substitute the upper limit [tex]\(x = d^3\)[/tex] and the lower limit [tex]\(x = 3\)[/tex] into the expression [tex]\(\frac{1}{3}\)[/tex].
3. Evaluation:
When we substitute the upper and lower limits, we get:
[tex]\[
\frac{1}{3} \times d^3 - \frac{1}{3} \times 3
\][/tex]
4. Simplify:
Simplify the expression:
[tex]\[
\frac{d^3}{3} - \frac{3}{3}
\][/tex]
5. Final Result:
[tex]\[
\frac{d^3}{3} - 1
\][/tex]
Thus, the final result of [tex]\(\left. \frac{1}{3} \right|_{3}^{d^3}\)[/tex] is:
[tex]\[
\frac{d^3}{3} - 1
\][/tex]
