Final answer:
To find the area bound by the curve f(x) = |x| and the x-axis between x = -3 and x = 2, we need to find the integral of the absolute value function within this interval.
Step-by-step explanation:
To find the area bound by the curve f(x) = |x| and the x-axis between x = -3 and x = 2, we need to find the integral of the absolute value function within this interval.
The function f(x) = |x| can be split into two cases: f(x) = x for x >= 0, and f(x) = -x for x < 0. We integrate each case separately within the given interval and take the sum of the absolute values of their results.
For the interval -3 to 0, the integral of f(x) = -x is given by -∫x dx = -∫-x dx = -(x^2/2) evaluated from -3 to 0.
For the interval 0 to 2, the integral of f(x) = x is given by ∫x dx = x^2/2 evaluated from 0 to 2.
Adding the absolute values of these two results gives us the area bound by the curve and the x-axis within the given interval