Question

use appropriate formulas from geometry to evaluate the integral $int_{1.5}^{9}(-4)dx$. write the exact answer. do not round.

Explanation:

Step1: Recall integral - geometry relation

The integral $\int_{a}^{b}c\ dx$ represents the signed - area of a rectangle with height $c$ and base $b - a$. Here $a = 1.5$, $b = 9$, and $c=-4$.

Step2: Calculate the base length

The base length of the rectangle is $b - a=9 - 1.5 = 7.5$.

Step3: Calculate the area

The area of the rectangle is $A = c\times(b - a)=-4\times7.5=-30$.

Answer:

$-30$