Problem

Suppose $\int_{2}^{13} f(x) d x=14$. Find $\int_{2}^{13} 5 f(x) d x$
\[
\int_{2}^{13} 5 f(x) d x=
\]

Answer

Expert–verified
Hide Steps
Answer

Final Answer: \(\boxed{70}\)

Steps

Step 1 :Given that \(\int_{2}^{13} f(x) d x=14\)

Step 2 :We need to find \(\int_{2}^{13} 5 f(x) d x\)

Step 3 :Since the integral of a constant times a function is the constant times the integral of the function, we can simply multiply the given integral by 5 to find the answer

Step 4 :Let the constant be 5 and the integral of the function f(x) from 2 to 13 be 14

Step 5 :So, \(\int_{2}^{13} 5 f(x) d x = 5 \times 14 = 70\)

Step 6 :Final Answer: \(\boxed{70}\)

link_gpt