Question is to calculate the area bounded by a cubic and the $x$-axis. Requires finding the roots by solving a cubic equation. Calculator question
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", "advice": "See 13.3, 14.1, and 14.3 for background on areas and (in)definite integration. See previous lectures for differentiation and integration.
\n\n\n\nAs this is a trickier question, here is some detailed advice:
\n1) Remember to estimate the answer, to help detect errors.
\n\n\n2) To find the minimum and maximum $x$-coordinates of the regions, you need to solve to $f(x)=0$. See Maths 1 for background on this. One of the solutions is 0 and the other roots are $\\var{xmax}$ and $\\var{xmin}$.
\nI label these numbers $a$ and $b$ (so I don't have to keep writing them). Also, use your calculator's memory abilities so you don't have to type the numbers over and over again.
\n\n\n3) I then set up the appropriate integral(s) to calculate the area:
\nArea $ = \\displaystyle \\int_{b}^0 \\simplify{{a}x^3+{b}x^2+{c}x} \\, dx - \\int^{a}_0 \\simplify{{a}x^3+{b}x^2+{c}x} \\, dx$
\n\n\n4) After doing the integration and plugging-in the numbers, you should get $\\var{area_total2}$, which is $\\var{area_total}$, to 3.s.f.
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\nThis is the graph of the function $f(x)=\\simplify{{a}x^3+{b}x^2+{c}x}$.
\n\nWhat is the area bounded by the graph and the $x$-axis (i.e. the total area of the shaded regions)? [[0]]
\nHint: you need to determine the $x$-intercepts before you can do any integration.
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