IB Maths AA SL AA 5.3 practice question

Paper 2, calculatorMedium6 marks

The curve $C$ has equation $y=f(x)$ where

f(x)=x^2-x-2.

(a)

Find the $x$ -coordinates of the points where $C$ intersects the $x$ -axis.

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(b)

Consider the region between $C$ and the $x$ -axis from $x=-2$ to $x=3$

(i)

Write down an expression, as a sum or difference of definite integrals of $f$ for the total area of this region. Do not use absolute-value notation.

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(ii)

Hence determine the total area exactly.

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