the function f(x)=3 - |3 + x| is graphed belo...
the function f(x)=3 - |3 + x| is graphed below. use geometric formulas to evaluate the following definite integral. ∫_{-6}^{0}(3 - |3 + x|) dx enter an exact answer.
Answer
# Explanation:
## Step1: Identify geometric shape
The graph of \(y = 3-|3 + x|\) from \(x=-6\) to \(x = 0\) forms a triangle.
## Step2: Determine base and height
The base of the triangle is \(b=6\) (since \(0-(-6)=6\)), and the height \(h = 3\).
## Step3: Apply triangle - area formula
The area of a triangle is \(A=\frac{1}{2}bh\). Substituting \(b = 6\) and \(h=3\) into the formula, we get \(A=\frac{1}{2}\times6\times3\).
# Answer:
9