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

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(52800) (Show Source): You can put this solution on YOUR website!
.

Plot y = (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) (Show Source): You can put this solution on YOUR website!

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.
RELATED QUESTIONS
Find the area of the region bounded by the y-axis, x-axis and the line y=−2x+4. (answered by math_helper,MathLover1)
Find the area of the region bounded by the x and y axes and the line 2x-3y... (answered by macston,solver91311)
find the area of the region bounded by two axes and the line... (answered by Fombitz)
Find the area of the region bounded by the x and y axes and the line y= 2x... (answered by sachi)
The area bounded by the lines x=0, x=2, x+y=4 and x-y=4 is revolved about the line x=4.... (answered by robertb)
find the area bounded by y^2=4x and... (answered by ikleyn)
the area bounded by the curves y=(x^3)/4, x+y=4 and y=0 is to be revolved about the... (answered by Alan3354)
the area bounded by the curves y=(x^3)/4, x+y=4 and y=0 is to be revolved about the... (answered by math_helper)
Find the area or the region bounded by the curves y = x^3 and y =... (answered by math_helper)