(1 point)
Given that $7 \leq f(x) \leq 8$ for $-8 \leq x \leq 5$, use property 8 of Section 5.2 of the Stewart Essential Calculus textbook to estimate the value of $\int_{-8}^{5} f(x) d x$ $\square \leq \int_{-8}^{5} f(x) d x \leq \square$
Note: You can earn partial credit on this problem.
Answer
Simplifying the above expression, we get $\boxed{91} \leq \int_{-8}^{5} f(x) d x \leq \boxed{104}$
Step 1 ：Given that $7 \leq f(x) \leq 8$ for $-8 \leq x \leq 5$, we can use property 8 of Section 5.2 of the Stewart Essential Calculus textbook to estimate the value of $\int_{-8}^{5} f(x) d x$
Step 2 ：The property states that if $m \leq f(x) \leq M$ for $a \leq x \leq b$, then $m(b-a) \leq \int_{a}^{b} f(x) d x \leq M(b-a)$
Step 3 ：Substituting the given values, we get $7(5 - (-8)) \leq \int_{-8}^{5} f(x) d x \leq 8(5 - (-8))$
Step 4 ：Simplifying the above expression, we get $\boxed{91} \leq \int_{-8}^{5} f(x) d x \leq \boxed{104}$
