y = -627,3x2 + 92,656x

How do you calculate the area of this curved line?

 

asked Jan 9 in Other Math Topics by anonymous

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The area is given by summing the areas of rectangular strips of width dx and length y. The area of each strip is ydx and when dx is infinitesimally small the area is given by the integral ∫ydx. However, you also need limits so that the area is finite. These produce a definite integral ∫[low,high]ydx. The limits can be natural limits like an axis or a line. In this problem it seems likely that the x axis is the line, so we need to find out where the x axis is intercepted by the curve. The x axis is y=0, so -627.3x^2+92.656x=0, x(-627.3x+92.656)=0, therefore x=0 and 92.656/627.3=0.1477 approx. The integral is ∫(-627.3x^2+92.656x)dx=-627.3x^3/3+92.656x^2/2 [0,0.1477].

Because the lower limit is 0 we just plug in x=0.1477: area=0.3369 sq units approx.

answered Jan 9 by Rod Top Rated User (479,220 points)
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