the function f(x)=3 - |3 + x| is graphed below. use geometric formulas to evaluate the following definite…
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