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This is a non-calculator question.

", "advice": "

See Lecture 12.4, 12.5, 13.1 and 13.2 for background knowledge and examples. Two main pieces of advice:

1) Do a simple estimate to check for big mistakes.

2) Remember that you have to think about whether the area is a `positive area' or `negative area'. Thinking about mechanics/distances/changes in position is the most coherent way I know of thinking about this.

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Two quadratic graphs are sketched with some area beneath them shaded. Question is to determine the area of shaded regions using integration. The first graph's area is all above the $x$-axis. The second graph has some area above and some below the $x$-axis.

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{plotgraph(2,x21,x22,-5,25,a2,0,c2)}

This is the graph of the function $f(x) = \\simplify{{a2}*x^2+{c2}}$.

Use integration to calculate the area of the shaded region. Give your answer without any rounding.

[[0]]

{plotgraph(3,x31,x32,-6,15,a3,b3,0)}

This curve has equation $y = \\simplify{x^2-{a3+b3}*x + {a3*b3}}$.

(Remember this is a non-calculator question!)

Calculate the total area of the shaded regions. Give your answer without any rounding.

[[0]]

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