(Solved): Suppose \( f \) has absolute minimum value \( m \) and absolute maximum value \( M \). Between wha ...

Suppose \( f \) has absolute minimum value \( m \) and absolute maximum value \( M \). Between what two values must \( \int_{0}^{4} f(x) d x \) lie? (smaller value) (larger value) Which property of integrals allows you to make your conclusion? \[ \int_{a}^{b} f(x) d x=-\int_{b}^{a} f(x) d x \] If \( m \leq f(x) \leq M \) for \( a \leq x \leq b \), then \( m(b-a) \leq \int_{a}^{b} f(x) d x \leq M(b-a) \). \[ \int_{a}^{c} f(x) d x+\int_{c}^{b} f(x) d x=\int_{a}^{b} f(x) d x \] If \( f(x) \geq 0 \) for \( a \leq x \leq b \), then \( \int_{a}^{b} f(x) d x \geq 0 \) \[ \int_{a}^{a} f(x) d x=0 \]