Evaluate the integral using the following values.
\[
\begin{array}{l}
\int_{4}^{8} x^{3} d x=960, \int_{4}^{8} x d x=24, \int_{4}^{8} d x=4 \\
\int_{4}^{8} \frac{1}{8} x^{3} d x
\end{array}
\]
Answer
Final Answer: The integral of \( \frac{1}{8} x^{3} \) from 4 to 8 is \( \boxed{120} \).
Step 1 ：The integral of a constant times a function is equal to the constant times the integral of the function.
Step 2 ：Therefore, to find the integral of \( \frac{1}{8} x^{3} \) from 4 to 8, we can multiply the given integral of \( x^{3} \) from 4 to 8 by \( \frac{1}{8} \).
Step 3 ：Given that the integral of \( x^{3} \) from 4 to 8 is 960, we multiply this by \( \frac{1}{8} \) to get the integral of \( \frac{1}{8} x^{3} \) from 4 to 8.
Step 4 ：Doing the multiplication, we get \( 960 \times \frac{1}{8} = 120 \).
Step 5 ：Final Answer: The integral of \( \frac{1}{8} x^{3} \) from 4 to 8 is \( \boxed{120} \).
