Question

homework 1: 1.1-1.4 review
score: 5/17 answered: 2/13
question 3
evaluate the integral below by interpreting
it in terms of areas in the figure.
the areas of the labeled regions are
a1=5, a2=3, a3=1 and a4=1
v = \\(\int_{3}^{7} |f(x)| \\, dx\\)
v =
enter your answer as a whole number
question help: video 1 video 2
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Explanation:

Step1: Split integral by absolute value

The integral $\int_{3}^{7} |f(x)| dx$ can be split into two intervals where $f(x)$ is negative then positive: $\int_{3}^{5} |f(x)| dx + \int_{5}^{7} |f(x)| dx$

Step2: Replace absolute value with area

For $3\leq x\leq5$, $f(x)$ is negative, so $|f(x)|$ corresponds to area A2. For $5\leq x\leq7$, $f(x)$ is positive, so $|f(x)|$ corresponds to area A3.
$\int_{3}^{5} |f(x)| dx = A2 = 3$, $\int_{5}^{7} |f(x)| dx = A3 = 1$

Step3: Sum the two areas

Add the values of the two areas: $3 + 1$

Answer:

4