7 The diagram below shows the graph of the curve that has equation \(y = x ^ { 2 } - 3 x + 2\) along with two shaded regions.
\includegraphics[max width=\textwidth, alt={}, center]{f87d1b36-26db-4a0b-b9ec-d7d82a396aba-08_646_711_408_667}
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- State the coordinates of the points \(A , B\) and \(C\).
7 - Katy is asked by her teacher to find the total area of the two shaded regions.
Katy uses her calculator to find \(\int _ { 0 } ^ { 2 } \left( x ^ { 2 } - 3 x + 2 \right) \mathrm { d } x\) and gets the answer \(\frac { 2 } { 3 }\)
Katy's teacher says that her answer is incorrect.
7 - Show that the total area of the two shaded regions is 1
Fully justify your answer.
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- (ii) Explain why Katy's method was not valid.