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This is a non-calculator question.

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

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

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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.

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.

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

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

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

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

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(Remember this is a non-calculator question!)

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