Suppose $\int_{2}^{4} f(x) d x=-5, \int_{2}^{7} f(x) d x=-4$, and $\int_{2}^{7} g(x) d x=2$. Evaluate the following integrals.
$\int_{7}^{2} g(x) d x=-2$
(Simplify your answer.)
\[
\int_{2}^{7} 8 g(x) d x=\square
\]
(Simplify your answer.)
Answer
Final Answer: The value of the integral \(\int_{2}^{7} 8 g(x) d x\) is \(\boxed{16}\)
Step 1 ：Given that \(\int_{2}^{7} g(x) d x=2\)
Step 2 ：We know that the integral of a constant times a function is equal to the constant times the integral of the function.
Step 3 ：Therefore, we can multiply the integral of g(x) from 2 to 7 by 8 to find the value of the second integral.
Step 4 ：So, \(\int_{2}^{7} 8 g(x) d x = 8 \times 2 = 16\)
Step 5 ：Final Answer: The value of the integral \(\int_{2}^{7} 8 g(x) d x\) is \(\boxed{16}\)
