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Integration and Its Applications · Paper 2 — Free Maths AA SL Practice Questions

1MasterySAQ-SIndefinite integrals and their propertiess8 marksPaper 2~12 min
The graph of f(x)=x3−2xf(x) = x^3 - 2x is shown for x∈Rx \in \mathbb{R}. The shaded region is bounded by the curve, the xx-axis, and the vertical lines x=−1x = -1 and x=2x = 2.
(a)
Find ∫f(x) dx\displaystyle\int f(x)\,dx. [2 marks]
(b)
Show that f(x)=x(x−2)(x+2)f(x) = x(x - \sqrt{2})(x + \sqrt{2}), and hence state the xx-values in the interval [−1,2][-1, 2] at which f(x)f(x) changes sign. [2 marks]
(c)
Calculate the total area of the shaded region. [4 marks]
diagram

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