Expert: NUR ARINA BASILAH BINTI KAMISAN - 8/10/2008

Question
Hi,

I'm having a hard time figuring out the problem.

Find the total area of the region enclosed by the graph of y=4x-x^3 and the x-axis.

I've tried to solve the problem using the definite interval. (the F look symbol). And I know I can't use the Reimann Sum to solve for it. (Or can you?)

Thanks!


Answer
hi emma,

if you want to find area of the region what you have to do is do some integration.in your problem,it mention the region is between the function y and x-axis.

first draw the graph.you can see from the graph that the point when y=0 is at x=-2,x=0 and x=2.so you have to find the area under this point.so you do integration from -2 to 0 and 0 to 2 or you also can do integration from 0 to 2 and then multiply it with 2 since the area will be the same.

area=2*(integration from 0 to 2)of 4x-x^3
when you integrate it you will get
area=2*(4x^2/2-x^4/4) and insert the value of integration which are 0 and 2
area=2*[(8-4)-0]
=2*4
=8unit^2

try to write it in mathematical form and draw the graph first any further information you can refer to this website: http://www.teacherschoice.com.au/Maths_Library/Calculus/area_under_a_curve.htm

good luck!!