SOLUTION: find the area bounded by y=6x-2x^3 and the line y-4=0

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Question 1143788: find the area bounded by y=6x-2x^3 and the line y-4=0
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52798) About Me  (Show Source):
You can put this solution on YOUR website!
.

    graph%28+330%2C+330%2C+-5%2C+5%2C+-5%2C+5%2C%0D%0A++++++++++6x+-+2x%5E3%2C+4%0D%0A%29


    Plot y = 6x+-+2x%5E3 (red)  and  y = 4 (green)



This area is the definite integral from -2 to 1 of the function y = 4 - (6x - 2x^3) = 2x^3 - 6x + 4.


Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


graph%28400%2C400%2C-4%2C4%2C-8%2C8%2C4%2C6x-2x%5E3%29

Algebra or a graphing calculator shows the points of intersection of the two graphs are at x=-2 and x=1; the cubic is below the constant in that interval.

So the area to be found is

integral from -2 to 1 of (4-(6x-2x^3)) dx

I will assume since you are asking this question that you know how to evaluate that integral.