The answer is 8au but I have a difficult time to understand why, can anybody explain? Question: Calculate the total area that is limited by the curve $$y = x^3 -4x$$ and the $x$-axis. Also if the question doesn't make sense, it's because I directly translated it so ask if there is something which doesn't make sense!
limited area of a curve
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$\begingroup$
calculus
curves
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0Everything that is in the example page which shows how to solve some of the upcomming questions but I get another answer on this one than it is in the solution. – 2017-01-09
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0What answer do you get? $0$? Something else? And how do you get that answer? – 2017-01-09
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0What is "8au" ? – 2017-01-09
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0yes I got 0 and not 8au, au = area units – 2017-01-09
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1You got $0$ because the area from $x = 0$ to $x = 2$ has been counted with the wrong sign. Areas are never negative, but integrals can be. You need to calculate the two areas separately, then add them together. – 2017-01-09
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0Still can't figure it out :/ Can you be so nice and post full solution? ): – 2017-01-09
1 Answers
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Draw a picture ! Then you should see that the area is given by
$\int_{-2}^0 (x^3-4x)dx +|\int_{0}^2 (x^3-4x)dx|$.