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Let f(x) = x² - x - 2 = (x - 2)(x + 1). To find ∫₋₂³|f(x)| dx, split the interval where f changes…

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

Let $f(x) = x^2 - x - 2 = (x - 2)(x + 1)$ . To find $\displaystyle\int_{-2}^{3}|f(x)|\,dx$ , split the interval where $f$ changes sign. Give the smaller root, the larger root, and the value of the integral to four decimal places.

Need a reminder? The key ideaShow

After $u = g(x)$ , change the limits to $g(a)$ and $g(b)$ . Split at a sign change or a joining point. For an odd function on $[-a, a]$ the integral is $0$ .

\displaystyle \int_a^b f(x)\,dx = \int_a^b f(a + b - x)\,dx.

The worked solution

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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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Let f(x) = x² - x - 2 = (x - 2)(x + 1). To find ∫₋₂³|f(x)| dx, split the interval where f changes…

The worked solution

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